
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
Solve the triangle given an angle $C$, the side opposite to it $c$, and the difference of the squares of the other two sides $p^{2}=b^{2}-a^{2}$. For example, $C=82^{\circ} 49^{\prime} 9.2^{\prime\prime}, \quad c=75 \mathrm{~cm}, \quad p^{2}=1406.25 \mathrm{~cm}^{2}$.

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