
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
If \( A \) is the area of a square inscribed in a circle of diameter 10, find \( A \).

If \( a+\frac{1}{a}=2 \), and \( S=a^{3}+\frac{1}{a^{3}} \), find \( S \).

An \( n \)-sided convex polygon has 14 diagonals. Find \( n \).

If \( d \) is the distance between the 2 points \( (2,3) \) and \( (-1,7) \), find \( d \).

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