The Collaborative International Dictionary of English v.0.48:

Muse \Muse\, v. i. [imp. & p. p. Mused; p. pr. & vb. n.
   Musing.] [F. muser to loiter or trifle, orig., to stand
   with open mouth, fr. LL. musus, morsus, muzzle, snout, fr. L.
   morsus a biting, bite, fr. mordere to bite. See Morsel, and
   cf. Amuse, Muzzle, n.]
   1. To think closely; to study in silence; to meditate.
      "Thereon mused he." --Chaucer.
      [1913 Webster]

            He mused upon some dangerous plot.    --Sir P.
                                                  Sidney.
      [1913 Webster]

   2. To be absent in mind; to be so occupied in study or
      contemplation as not to observe passing scenes or things
      present; to be in a brown study. --Daniel.
      [1913 Webster]

   3. To wonder. [Obs.] --Spenser. --B. Jonson.
      [1913 Webster]

   Syn: To consider; meditate; ruminate. See Ponder.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

musing \musing\ adj.
   Thinking long and intensely.

   Syn: brooding, broody, contemplative, meditative, pensive,
        pondering, reflective, ruminative.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

musing
    adj 1: deeply or seriously thoughtful; "Byron lives on not only
           in his poetry, but also in his creation of the 'Byronic
           hero' - the persona of a brooding melancholy young man";
           [syn: brooding, broody, contemplative,
           meditative, musing, pensive, pondering,
           reflective, ruminative]
    n 1: a calm, lengthy, intent consideration [syn:
         contemplation, reflection, reflexion, rumination,
         musing, thoughtfulness]

Moby Thesaurus II by Grady Ward, 1.0:

121 Moby Thesaurus words for "musing":
   Walter Mitty, absence of mind, absent, absentminded,
   absentmindedness, absorbed, absorption, abstracted, abstractedness,
   abstraction, advisement, bemused, bemusement, brooding,
   brown study, castle-building, close study, cogitative, cognitive,
   concentrating, concentration, concentrative, conceptive,
   conceptual, conceptualized, consideration, contemplating,
   contemplation, contemplative, contemplativeness, counsel, daydream,
   daydreamer, daydreaming, daydreamy, deep thought, deliberating,
   deliberation, deliberative, depth of thought, dream, dreamery,
   dreamfulness, dreaminess, dreaming, dreamlikeness, dreamy,
   drowsing, ecstatic, elsewhere, engrossed, engrossment,
   excogitating, fantasy, fantasying, faraway, fit of abstraction,
   half-awake, ideative, in a reverie, in the clouds, introspective,
   lost, lost in thought, lucubration, meditating, meditation,
   meditative, melancholy, mental, mooning, moonraking, muse, museful,
   musefulness, muted ecstasy, napping, nodding, noetic, oblivious,
   pensive, pensiveness, pipe dream, pipe-dreaming, pondering,
   prehensive, preoccupation, preoccupied, profound thought, rapt,
   reflecting, reflection, reflective, reflectiveness, reverie,
   revolving, ruminant, ruminating, rumination, ruminative, serious,
   sober, somewhere else, speculation, speculative, speculativeness,
   stargazing, study, taken up, thinking, thought, thoughtful,
   thoughtfulness, trance, transported, unconscious, weighing,
   wistful, wistfulness, woolgathering, wrapped in thought