
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 an inequality with respect to $x$: $\frac {ax-5}{x^{2}-a} < 0$, the solution set is denoted as $M$.
(1) Find the set $M$ when $a=4$;
(2) If $3 \in M$ and $5 \notin M$, determine the range of the real number $a$.

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