
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
Given triangle $PQR$ with altitude $PS$ drawn to $QR$, altitude $QT$ drawn to $PR$, and altitude $RU$ drawn to $PQ$, and given the lengths of $QR$, $PS$, and $QT$ are 10 units, 6 units, and 8 units respectively, find the area of triangle $PQR$.

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