
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 line $L: y = x + m$ intersects with the parabola $y^2 = 8x$ at points A and B (different from the origin),
(1) If line L passes through the focus of the parabola, find the length of segment $|AB|$;
(2) If $OA \perp OB$, find the value of $m$.

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