
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 triangle \(ABC\), the sine of angle \(A\) is equal to \(3/5\). Point \(M\) is taken on side \(AC\) such that \(CM = 15\), and point \(N\) is taken on side \(AB\) such that \(BN = 7\) and \(AN = AM\). \(T\) is the midpoint of \(NC\), and \(P\) is the midpoint of \(B\). Find the length of segment \(PT\).

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