
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 function $f(x) = x^2 + (2a-8)x$, the solution set of the inequality $f(x) \leq 5$ is $\{x|-1 \leq x \leq 5\}$.
1. Find the value of the real number $a$.
2. $f(x) \geq m^2 - 4m - 9$ holds for all $x \in \mathbb{R}$. Find the range of the real number $m$.

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