
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 $p$: For real number $x$, it satisfies $x-a<0$, and $q$: For real number $x$, it satisfies $x^2-4x+3\leq0$.  
(1) If $a=2$, and $p\land q$ is true, find the range of real numbers $x$.  
(2) If $p$ is a necessary but not sufficient condition for $q$, find the range of real numbers $a$.

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