
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 $f(x) = 3x^4 - 8x^3 - 18x^2 + a$,
1. Find the intervals of monotonicity for the function $f(x)$;
2. If the maximum value of $f(x)$ on the interval $[-1, 1]$ is 6, find the minimum value of $f(x)$ on this interval.

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