
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 two sets $A=\{x | x^2 \leq 3x + 10\}$ and $B=\{x | a + 1 \leq x \leq 2a + 1\}$.
(1) If $a = 3$, find $(\complement_{\mathbb{R}}A) \cup B$;
(2) If $A \cap B = B$, determine the range of the real number $a$.

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