
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 Cauchy problem for the system

$$
\begin{gathered}
\left\{\begin{array}{l}
\frac{d x}{d t} = 3 x + 8 y \\
\frac{d y}{d t} = -x - 3 y
\end{array}\right. \\
x(0) = 6, \quad y(0) = -2
\end{gathered}
$$

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