
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 $C: y^2 = 2px$ ($p>0$), $F$ is the focus of the parabola $C$, $A$ is a moving point on the parabola $C$. A perpendicular line to the directrix $l$ of the parabola is drawn through point $A$, with foot $Q$.
(1) If the line connecting point $P(0,4)$ and point $F$ exactly goes through point $A$, and $\angle PQF = 90^\circ$, find the equation of the parabola;
(2) Assume point $M(m,0)$ lies on the x-axis. To make the angle $\angle MAF$ always acute, find the range of the values of $m$.

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