
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 $ABC$, $\angle C = \frac{\pi}{3}$, and let $\angle BAC = \theta$. If there exists a point $M$ on line segment $BC$ (distinct from points $B$ and $C$) such that $\triangle BAM$ is folded over line $AM$ to obtain $\triangle B'A'M$, and the condition $AB' \perp CM$ is satisfied, then determine the range of values for $\theta$.

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