
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
Triangle \(PQR\) has \(PQ=13\), \(PR=14\) and \(QR=15\). Points \(X\) and \(Y\) are located on \(\overline{PQ}\) and \(\overline{PR}\), respectively, such that \(\overline{XY}\) is parallel to \(\overline{QR}\) and contains the center of the inscribed circle of triangle \(PQR\). Find \(XY\) in the form \(m/n\), where \(m\) and \(n\) are relatively prime positive integers, and compute \(m+n\).

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