
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 the function $f(x) = (ax-1)(x-1)$.  
(1) If the solution set of the inequality $f(x) < 0$ is $\{x|1 < x < 2\}$, find the value of the real number $a$;  
(2) When $a > 0$, solve the inequality $f(x) < 0$.

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