
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 a polynomial \( p(x) \) such that when divided by \( (x-2)(x-5) \), the remainder is a polynomial of degree less than 2. Given \( p(2) = 4 \) and \( p(5) = 9 \), find the remainder polynomial \( r(x) \).
A) \( \frac{4}{3}x + \frac{5}{3} \)
B) \( \frac{5}{3}x + \frac{2}{3} \)
C) \( \frac{5}{2}x + 1 \)
D) \( 2x + 5 \)

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