
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 functions $\alpha(x)$ and $\beta(x)$ satisfy the following conditions:

1) $\alpha(x)$ and $\beta(x)$ are $n$ times differentiable;

2) $\alpha^{(m)}\left(x_{0}\right) = \beta^{(m)}\left(x_{0}\right)$, where $m=0,1, \ldots, n-1$;
3) $\alpha^{(n)}(x) > \beta^{(n)}(x)$ for $x > x_{0}$.

Then the inequality $\alpha(x) > \beta(x)$ holds for $x > x_{0}$.

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