
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
Given a parabola $y^2 = 2px$ ($p > 0$) and a point $A(1, 2)$ on this parabola, the distance from point $A$ to point $B(x, 0)$ is equal to its distance to the line $x = -1$. Find the value of the real number $x$.

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