
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 the differentiable functions $f(x)$ and $g(x)$ on $\mathbb{R}$, when $x > 1$, $f'(x) > g'(x)$, and when $x < 1$, $f'(x) < g'(x)$, determine the relationship between $f(2) - f(1)$ and $g(2) - g(1)$.

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