
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 system of differential equations

$$
\left\{\begin{array}{l}
y_{1}^{\prime} = y_{2} + y_{3} \\
y_{2}^{\prime} = y_{1} + y_{3} \\
y_{3}^{\prime} = y_{1} + y_{2}
\end{array}\right.
$$

and find the particular solution given $x=0$, $y_{1}=1$, $y_{2}=2$, $y_{3}=0$.

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