
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
The area of an equilateral triangle is $50 \sqrt{12}$. If its perimeter is $p$, find $p$.

The average of $q, y, z$ is 14. The average of $q, y, z, t$ is 13. Find $t$.

If $7-24 x-4 x^{2} \equiv K+A(x+B)^{2}$, where $K, A, B$ are constants, find $K$.

If $C=\frac{3^{4 n} \cdot 9^{n+4}}{27^{2 n+2}}$, find $C$.

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