
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 following system of equations:

$$
\begin{aligned}
\sin x+\sin (x+y)+\sin (x+2 y) & =\sin \varphi \\
\cos x+\cos (x+y)+\cos (x+2 y) & =\cos \varphi
\end{aligned}
$$

Here, $\varphi$ represents a given angle.

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