
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
Given that the polynomial $g(x)$ satisfies $g(x + 1) - g(x) = 10x^2 + 2$ for all $x$, determine the leading coefficient of $g(x)$.

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