
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 \( f(x) = ax^3 + bx^2 + cx + d \), with \( 1 \leq f(-1) \leq 2 \), \( 1 \leq f(1) \leq 3 \), \( 2 \leq f(2) \leq 4 \), and \( -1 \leq f(3) \leq 1 \), find the range of \( f(4) \).

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