
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 $PQRS$ be a tetrahedron such that edges $PQ$, $PR$, and $PS$ join at $P$ and are mutually perpendicular. The lengths of $PQ$, $PR$, and $PS$ are $a$, $b$, and $c$ respectively. An external point $T$ is placed such that it makes an isosceles right triangle with $PR$ and $PS$ where $RT = ST = t$. Determine the area of triangle $QRS$.

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