
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 \( n \) (\( n \geqslant 2 \)) real numbers \( \theta_{1}, \theta_{2}, \cdots, \theta_{n} \) (\( \theta_{i} \in \left(0, \frac{\pi}{2}\right], 1 \leqslant i \leqslant n \)) that satisfy \( \sum_{i=1}^{n} \sin \theta_{i} \leqslant 1 \), find the maximum value of \( \prod_{i=1}^{n} \tan \theta_{i} \).

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