
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 that the function \( y = f(x) \) is a monotonically increasing function defined on \( \mathbf{R} \), and for any \( x \in \mathbf{R} \), \( f(5-x) = -f(-1+x) \), solve the inequality \(\left| f \left( x^{2} - 2x + 7 \right) \right| < f \left( x^{2} + 3a + 2 \right) \).

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