
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 a right-angled triangle ABC with a perimeter of $p$ and an area of $s$, where $\angle C=90^\circ$. Express the length of segment AB in terms of $p$ and $s$, and write a quadratic equation in one variable with the lengths of segments AC and BC as its roots.

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