
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
The sum of the roots $\tan \alpha$ and $\tan \beta$ of the equation $x^{2}+3ax+3a+1=0$ can be expressed in terms of the coefficients. Express the sum of the angles $\alpha$ and $\beta$ in terms of the coefficient $a$.

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