
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 continuous functions  $x(t),\ y(t)$  such that 

 $\ \ \ \ \ \ \ \ \ x(t)=1+\int_{0}^{t}e^{-2(t-s)}x(s)ds$ 

 $\ \ \ \ \ \ \ \ \ y(t)=\int_{0}^{t}e^{-2(t-s)}\{2x(s)+3y(s)\}ds$ 

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