
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
Consider the functions $f(x)=mx+n$ and $h(x)=px^2 + qx + r$, where $m, n, p, q, r$ are real numbers. Determine the condition under which the equation $f(h(x)) = h(f(x))$ holds true.
**A)** $m = p \text{ and } n = 0$  
**B)** $m = p \text{ and } q = r$  
**C)** $q = 2pm + r$  
**D)** $r = 2n + p$  
**E)** $p = q \text{ and } m = n$

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