
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
Right triangle \(ABC\) has legs \(AB = 8\) cm and \(AC = 15\) cm, and a right angle at \(A\). Within triangle \(ABC\), a square is placed such that one side lies along the hypotenuse \(BC\) of the triangle, and a vertex of the square touches each of the legs of the triangle \(ABC\). Find the length of a side of the square, \(s\), in cm. Express your answer as a common fraction.

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