
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 a right triangle $PQR$, where $PQ$ is the hypotenuse, another right triangle $PQT$ is constructed outside triangle $PQR$ such that $PQ$ is shared as the hypotenuse for triangle $PQT$. If $\overline{QR} = 2$, $\overline{PR} = a$, and $\overline{PT} = 3$, find the length of $\overline{QT}$.
A) $\sqrt{a^2 + 3}$
B) $\sqrt{a^2 - 5}$
C) $\sqrt{a^2 + 5}$
D) $a^2 + 5$

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