
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 the ellipse \(\frac{x^{2}}{4}+y^{2}=1\) with left and right foci \(F_{1}\) and \(F_{2}\) respectively, let \(M\) be a point on the ellipse, and let \(I\) be the incenter of \(\triangle M F_{1} F_{2}\). Determine the value of \(\overrightarrow{O I} \cdot \overrightarrow{O M}\).

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