
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
Let $a$, $b$, and $c$ be acute angles such that
\begin{align*}
2 \sin^2 a + 4 \sin^2 b + 3 \sin^2 c &= 2, \\
5 \sin 2a - 4 \sin 2b + \sin 2c &= 0.
\end{align*}
Find $a + 2b + c,$ as measured in radians.

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