
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 the inequality concerning $x$: $ax^2 -(a+2)x + 2 < 0$.
(1) Solve the inequality when $a = -1$.
(2) Solve the inequality for $a \in \mathbb{R}$.

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