
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
A subsidiary of Fujian Refinery refines crude oil into gasoline, which requires cooling and heating of the crude oil. If the temperature of the crude oil in the $x$-th hour is given by the function $f(x) = \frac{1}{3}x^3 - x^2 + 8 \ (0 \leq x \leq 5)$, what is the minimum instantaneous rate of change of the crude oil temperature?

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