
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 equations:

$$
\left.\begin{array}{l}
\dot{x}=5 x-3 y+2 e^{3 t} \\
\dot{y}=x+y+5 e^{-t}
\end{array}\right\}
$$

And solve the system of equations:

$$
\dot{x}=y ; \dot{y}=z, \dot{z}=x
$$

And solve the system of equations:

$$
\left.\begin{array}{l}
\dot{x}=x+z-y ; \\
\dot{y}=x+y-z \\
\dot{z}=2 x-y
\end{array}\right\}
$$

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