
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
Find the maximum value of \( S = \sin^2 \theta_1 + \sin^2 \theta_2 + \cdots + \sin^2 \theta_n \), where \( 0 \leq \theta_i \leq \pi \) and \( \theta_1 + \theta_2 + \cdots + \theta_n = \pi \).

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