
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 the parabola $y^2 = 2px$ ($p > 0$) passes through point A($2$, $y_0$) and the distance from point A to its axis is $4$.
(1) Find the equation of the parabola.
(2) Line $l$: $y = x + m$ intersects the parabola at two distinct points P and Q. If $OP \perp OQ$, find the value of the real number $m$.

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