
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
In a triangle with sides \(a, b, c\) and angles \(\alpha, \beta, \gamma\), the equality \(3\alpha + 2\beta = 180^\circ\) holds. The sides \(a, b, c\) are opposite to angles \(\alpha, \beta, \gamma\) respectively. Find the length of side \(c\) given that \(a = 2\) and \(b = 3\).

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