
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 parabola has its vertex at the origin, is symmetric about the x-axis, and passes through point $M(-2, 2\sqrt{2})$. Its focus is F.
(1) Find the equation of the parabola and the coordinates of the focus.
(2) A line $l$ passes through F and has a slope of 45°. It intersects the parabola at points A and B. Find the length of the chord $|AB|$.

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