
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 that $O$ is the coordinate origin, $A(2\cos\alpha, 2\sin\alpha)$, $B(\cos\alpha-\sqrt{3}\sin\alpha, \sin\alpha+\sqrt{3}\cos\alpha)$, and $\overrightarrow{OP}=\overrightarrow{OA}+\overrightarrow{OB}$, with a fixed point $M(4,0)$, then the equation of line $MP$ when $\angle PMO$ is at its maximum value is ______.

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