
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
Let \( M \) be any point on the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) (where \( a > b > 0 \)), and \( F_{1} \) and \( F_{2} \) be its two foci. Let \( \angle F_{1}M F_{2} = \theta \).
1. Find the maximum value of \( \theta \);
2. Find the maximum value of \( \sin \theta \).

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