
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 \( n \geq 5 \) be an integer. Determine the largest integer \( k \) such that a polygon with \( n \) vertices and exactly \( k \) interior \( 90^{\circ} \) angles exists. (The polygon does not have to be convex, but the edges must not intersect themselves).

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