
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 positive integer \( n \), find the smallest positive number \( \lambda \) such that for any \( \theta_{i} \in \left(0, \frac{\pi}{2}\right) (i=1, 2, \cdots, n) \), as long as \( \tan \theta_{1} \cdot \tan \theta_{2} \cdots \tan \theta_{n} = 2^{\frac{n}{2}} \), we have \( \cos \theta_{1} + \cos \theta_{2} + \cdots + \cos \theta_{n} \leq \lambda \).

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