
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

$$
\begin{cases}x^{\prime}=x+2 y-9 t, & x(0)=1 \\ y^{\prime}=2 x+y+4 e^{t}, & y(0)=2\end{cases}
$$

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