
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 differential equation (with the initial condition):
$$
\left\{\begin{array}{l}
y^{\prime}(t)-2 y(t)=e^{t} \\
y(0)=0 \\
t>0
\end{array}\right.
$$

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