
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
In a plane, two circles with radii 10 units and 7 units have centers 15 units apart. At a point \( P \) of intersection of these circles, a line is drawn such that the chords \( QP \) and \( PR \) intersecting the two circles are of equal lengths. Another circle passes through \( P \) and intersects the first and second circles at points \( S \) and \( T \) respectively, such that \( PS = PT = QP \). Find the square of the length of \( QP \).

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