
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
Find a value of \( x \) satisfying the equation \( x^2 + (b+1)^2 = (a+1 - x)^2 \).
A) \(\frac{a^2 - b^2 + 2a + 2b}{2(a+1)}\)
B) \(\frac{a^2 - b^2 + 2a - 2b}{2(a+1)}\)
C) \(\frac{a^2 - b^2 - 2a - 2b}{2(a+1)}\)
D) \(\frac{b^2 - a^2 + 2a - 2b}{2(a+1)}\)
E) \(\frac{a^2 + b^2 + 2a - 2b}{2(a+1)}\)

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