
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 integro-differential equation:

$$
\begin{gathered}
\varphi^{\prime \prime}(x) + \int_{0}^{x} e^{2(x-t)} \varphi^{\prime}(t) \, d t = e^{2x} \\
\varphi(0) = \varphi^{\prime}(0) = 0
\end{gathered}
$$

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