
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 integral equation:
a) \(y(\tau)=\int_{0}^{t} y(\tau) \, d\tau + 1\);
b) \(\int_{0}^{t} y(\tau) \sin(t-\tau) \, d\tau = 1 - \cos t\).

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