
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 $x$, and a point $M$ on its terminal side has coordinates $(1,\sqrt{3})$. Then, $\tan (\alpha +\frac{\pi }{3})=$ ______.

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