
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 solution set of the inequality $x^2 \leq 5x - 4$ be $A$.
(1) Find the set $A$;
(2) Let the solution set of the inequality $x^2 - (a+2)x + 2a \leq 0$ ($a \geq 2$) concerning $x$ be $M$. If condition $p$: $x \in M$, condition $q$: $x \in A$, and $p$ is a sufficient condition for $q$, find the range of the real number $a$.

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