
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
If \( b_0 = \sin^2 \left(\frac{\pi}{60}\right) \) and
\[
b_{m + 1} = 4b_m (1 - b_m) \text{ for } m \geq 0,
\]
find the smallest positive integer \( m \) such that \( b_m = b_0 \).

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