
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 $y^2=2px$ ($p>0$), and point $M(2, y_0)$ is on the parabola, $|MF|= \frac {5}{2}$.  
(1) Find the equation of the parabola.  
(2) Let the coordinates of point A be $( \frac {2}{3}, 0)$, find the coordinates of point B on the parabola that is closest to point A and the corresponding distance $|BA|$.

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