
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
A point $(x, y)$ is to be chosen on the coordinate plane so that it is equally distant from the y-axis, the line $x+y=1$, and the line $y=3x$. Determine the x-coordinate of such a point.
A) $\frac{1}{5}$
B) $\frac{2}{5}$
C) $\frac{1}{3}$
D) $\frac{1}{4 + \sqrt{10} - \sqrt{2}}$

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