
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
Write the equation of a parabola that is symmetric with respect to the $x$-axis, with its vertex at the origin, given that the parabola passes through the point $A(2,2)$.

Find the length of the chord passing through the point $M(8,0)$ and inclined at an angle of $60^{\circ}$ to the $x$-axis.

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