
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 the Cartesian coordinate plane, the coordinates of point $P$ are $\left( \frac{3}{5}, \frac{4}{5}\right)$, and point $Q$ lies in the third quadrant with $|OQ|=1$ and $\angle POQ = \frac{3\pi}{4}$. Determine the $x$-coordinate of point $Q$.

A) $-\frac{7 \sqrt{2}}{10}$
B) $-\frac{3 \sqrt{2}}{5}$
C) $-\frac{7 \sqrt{2}}{12}$
D) $-\frac{8 \sqrt{2}}{13}$

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