
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
For the inequality $\frac{ax-5}{x-a} < 0$, the solution set is denoted as M.
1. Find the set M when $a=1$.
2. Determine the range of the real number $a$ such that $3 \in M$ but $5 \notin M$.

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