
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
Given \( a_{1} = \frac{\pi}{6} \), and \( a_{n} \in \left(0, \frac{\pi}{2} \right) \) satisfying \( \tan a_{n+1} \cdot \cos a_{n} = 1 \) for \( n \geq 1 \). If \( \prod_{k=1}^{m} \sin a_{k} = \frac{1}{100} \), find \( m \).

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