
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 the functions $f(x)$ and $g(x)$ be differentiable on $\mathbb{R}$, and their derivatives satisfy $f'(x) > g'(x)$. Then, for $a < x < b$, which of the following inequalities are correct:
1. $f(x) > g(x)$;
2. $f(x) < g(x)$;
3. $f(x) + g(b) < g(x) + f(b)$;
4. $f(x) + g(a) > g(x) + f(a)$.

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