
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
A circular pizza with a diameter of $16\text{ cm}$ is divided into four equal sectors. Determine the square of the length of the longest line segment that can be drawn within one of these sectors.

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