
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
Let triangle $PQR$ be a right triangle in the xy-plane with a right angle at $R$. The lengths of legs $PR$ and $RQ$ are given as 24 and 73 respectively, and $PQ$ (hypotenuse) becomes 75. The median through $P$ lies along the line $y = 3x + 4$ and the median through $Q$ lies along the line $y = -x + 5$. Find the area of triangle $PQR$.

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