
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 functions  $ f(x),\ g(x)$  satisfying the following equations.

(1)  $ f'(x) \equal{} 2f(x) \plus{} 10,\ f(0) \equal{} 0$ 

(2)  $ \int_0^x u^3g(u)du \equal{} x^4 \plus{} g(x)$ 

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