
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
Find the particular solution of the system of differential equations

$$
\frac{d x}{d t} + 2x + y = \sin t
$$
$$
\frac{d y}{d t} - 4x - 2y = \cos t
$$

that satisfies the initial conditions \( x(\pi) = 1 \) and \( y(\pi) = 2 \).

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