
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
Find the solution to the Cauchy problem for an equation of the form:
\[ y^{(n)}(x) = F(x) \]
Specifically,
\[ y'''(x) = 24x, \]
with the initial conditions
\[ y(0) = 3, \, y'(0) = 2, \, y''(0) = 4. \]

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