
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In triangle \( \triangle ABC \), \( \angle C = \frac{\pi}{3} \). Let \( \angle BAC = \theta \). Suppose there exists a point \( M \) on segment \( BC \) (different from points \( B \) and \( C \)). By reflecting \( \triangle BAM \) along line \( AM \), we obtain \( \triangle B'AM \) such that \( AB' \perp CM \). What is the range of possible values for \( \theta \)?

Present the answer in LaTex format: \boxed{Your answer}
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