
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 sets $P=\{x|a+1\leq x\leq 2a+1\}$, $Q=\{x|x^2-3x\leq 10\}$.  
(1) If $a=3$, find $(\complement_R P) \cap Q$;  
(2) If $P\cup Q=Q$, find the range of the real number $a$.

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