
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 value of $x$ satisfying the equation $x^2 + b^2 + c^2 = (a - x)^2 + c^2$ where $a$, $b$, and $c$ are different non-zero constants, is:
A) $\frac{a^2 + b^2}{2a}$
B) $\frac{b^2 - a^2}{2a}$
C) $\frac{a^2 - b^2}{2a}$
D) $\frac{c^2 - a^2}{2a}$
E) $\frac{a - b}{2}$

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