
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
Let the parabola $y = ax^2 + bx + c$ pass through the points $A(-1, -3)$, $B(4, 2)$, and $C(0, 2)$. Let $P$ be a moving point on the axis of symmetry of the parabola. If $P A + P C$ reaches its minimum value at the point $P$ with coordinates $(m, n)$, find $n$.

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