
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) In the diagram, $\triangle PQR$ is right-angled at $R$. If $PQ = 25$ and $RQ = 24$, determine the perimeter and area of $\triangle PQR$.

(b) In the diagram, $\triangle ABC$ is right-angled at $C$ with $AB = c$, $AC = b$, and $BC = a$. Also, $\triangle ABC$ has a perimeter of 144 and an area of 504. Determine all possible values of $c$.

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