
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 $p: \frac{x+1}{x-2} > 2$, $q: x^{2}-ax+5 > 0$.
$(1)$ If $p$ is true, find the range of $x$;
$(2)$ If $p$ is a sufficient but not necessary condition for $q$, find the range of real number $a$.

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