
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
Given that $G$ is the centroid of triangle $ABC$ and $\overrightarrow{AG} \cdot \overrightarrow{BG} = 0$, if $\frac{1}{\tan A} + \frac{1}{\tan B} = \frac{\lambda}{\tan C}$, find the value of the real number $\lambda$.

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