
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 \( b > 0 \), and let \( R(x) \) be a polynomial with integer coefficients such that
\[ R(2) = R(4) = R(6) = R(8) = b \]
and
\[ R(3) = R(5) = R(7) = R(9) = -b. \]
What is the smallest possible value of \( b \)?

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