
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
Solve the equations:
1) \( y'' + 6y' + 5y = 25x^2 - 2 \)
2) \( y'' - 2y' + 10y = 37 \cos 3x \)
3) \( y'' - 6y' + 9y = 3x - 8e^x \)
4) \( y''' + 4y' = 8e^{2x} + 5e^x \sin x \)

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