
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 the focus of the parabola $y^{2}=4x$ is $F$, a line $l$ passing through point $F$ intersects the parabola at two points $A$ and $B$. If point $M$ satisfies $\overrightarrow{OM}= \frac {1}{2}( \overrightarrow{OA}+ \overrightarrow{OB})$, a line perpendicular to the $y$-axis passing through $M$ intersects the parabola at point $P$. If $|PF|=2$, find the x-coordinate of point $M$.

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