
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
Formulate the integral equation corresponding to the differential equation

$$
y'' + x y' + y = 0
$$

and the initial conditions

$$
y(0)=1, \quad y'(0)=0
$$

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