
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 a right angle at $Q$. Point $S$ is the foot of the altitude from $Q$, $PS=5$, and $SR=7$. What are the area and the perimeter of $\triangle PQR$?
A) Area = $6$, Perimeter = $109$
B) Area = $6\sqrt{35}$, Perimeter = $12$
C) Area = $18$, Perimeter = $36$
D) Area = $6\sqrt{35}$, Perimeter = $56\sqrt{3}$
E) Area = $6\sqrt{35}$, Perimeter = $\sqrt{109} + \sqrt{35} + 12$

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