
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 $M = \{x \mid x^2 - 3x \leq 10\}$ and $N = \{x \mid a-1 \leq x \leq 2a+1\}$.
(1) Find $ (\complement_{\mathbb{R}} M) \cup N $ when $a = 2$;
(2) If $M \cup N = M$, determine the range of the real number $a$.

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