
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 paper equilateral triangle $ABC$ has side length 15. The paper triangle is folded so that vertex $A$ touches a point on side $\overline{BC}$ a distance 10 from point $B$, and vertex $B$ touches a point on side $\overline{AC}$ a distance 3 from point $C$. Find the square of the length of the line segment along which the triangle is folded.

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