
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 \((x, y)\) in the coordinate plane must be equidistant from the x-axis, the y-axis, and the line \(2x + 3y = 6\). What is the x-coordinate of this point?
A) \(\frac{1}{2}\)  
B) \(\frac{6}{5}\)  
C) \(2-\sqrt{2}\)  
D) \(1\)  
E) \(\text{Not uniquely determined}\)

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