
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 \( a_{1}, a_{2}, \ldots, a_{2019} \in [-1,1] \) with \( a_{1} + a_{2} + \ldots + a_{2019} = 0 \), find the maximum and minimum values of \( f = a_{1}^3 + a_{2}^3 + \ldots + a_{2019}^3 \).

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