
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 $y^2 = 4x$ and the line $y = 2x + m$. The chord formed by the intersection of the parabola and the line has a length of $3\sqrt{5}$.

(1) Find the value of $m$.
(2) Let $P$ be a point on the $x$-axis such that the area of $\triangle ABP$ is $9$. Find the coordinates of point $P$.

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