
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
A function \( f(x) \) defined on \(\mathbf{R}\) satisfies: 
1. \( f(2+x) \) is an even function.
2. \( f(x) \) is an increasing function on \((-\infty, +2]\).

Solve the inequality \( f\left(a^{2}+3a+2\right) < f\left(a^{2}-a+2\right) \).

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