
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 
$$
f(x) = 3 \lg (x+2) - \log_{2} x,
$$

and the set \( M = \{ n \in \mathbf{Z} \mid f(n^3 - 3n^2 - 10n + 32) \geq 0 \} \), find \( M \).

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