
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 $y^2=2px$ ($p>0$). A line $l$ passing through the moving point M($a$, $0$) with a slope of 1 intersects the parabola at two distinct points A and B, such that $|AB| \leq 2p$.
(1) Find the range of values for $a$;
(2) If the perpendicular bisector of the line segment AB intersects the x-axis at point N, find the maximum value of the area of triangle $\triangle NAB$.

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