
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 point $P(0,1)$, on the ellipse $\dfrac{x^2}{4} + y^2 = m (m > 1)$, there are two points $A$ and $B$ satisfying $\overrightarrow{AP} = 2\overrightarrow{PB}$. The absolute value of the x-coordinate of point $B$ is maximized when $m=$ ______.

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