
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 the Cartesian coordinate system xOy, it is known that the vertex of angle $\alpha$ coincides with point O, its initial side coincides with the non-negative half-axis of the x-axis, and a point M on its terminal side has coordinates (-1, $\sqrt{3}$). Then, $\tan(\alpha + \frac{\pi}{4}) = \_\_\_\_\_$.

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