
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 $p$: The real number $x$ satisfies $x^{2}-5ax+4a^{2} < 0$ (where $a > 0$), $q$: The real number $x$ satisfies $2 < x \leqslant 5$.

$(1)$ If $a=1$ and $p \land q$ is true, find the range of the real number $x$;

$(2)$ If $\neg q$ is a necessary but not sufficient condition for $\neg p$, find the range of the real number $a$.

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