
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 \( h(x) \) and \( j(x) \) be two monic cubic polynomials, and let \( s \) be a real number. Two of the roots of \( h(x) \) are \( s + 2 \) and \( s + 6 \). Two of the roots of \( j(x) \) are \( s + 4 \) and \( s + 8 \), and
\[ 2(h(x) - j(x)) = s \]
for all real numbers \( x \). Find \( s \).

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