
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
Let \( f: \mathbf{R} \rightarrow \mathbf{R} \) be a continuous function with \( \int_{0}^{1} f(x) f^{\prime}(x) \, dx = 0 \) and \( \int_{0}^{1} f(x)^{2} f^{\prime}(x) \, dx = 18 \). What is \( \int_{0}^{1} f(x)^{4} f^{\prime}(x) \, dx \)?

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