
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 propositions p: $x^2 \leq 5x - 4$, and q: $x^2 - (a+2)x + 2a \leq 0$  
(1) Find the range of $x$ for proposition p;  
(2) If p is a necessary but not sufficient condition for q, find the range of $a$.

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