
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 function $f(x) = x^3 + ax^2 - 9x - 1$;  
(Ⅰ) If $x = -1$ is an extremum point of the function $f(x)$, find: (1) the value of $a$; (2) the maximum and minimum values of the function $f(x)$ on the interval $[-2, 5]$.  
(Ⅱ) Determine whether there exists a real number $a$ such that $f(x)$ is monotonically increasing on $\mathbb{R}$; if it exists, find the range of $a$; if not, explain why.

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