
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
(1) Find the solution set $A$ for the inequality $x^2 \leq 5x - 4$;  
(2) Let the solution set for the inequality $(x-a)(x-2) \leq 0$ with respect to $x$ be $M$. If $M \subseteq A$, find the range of the real number $a$.

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