
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 the graph of the tangent function, write the set of $x$ values that satisfy the following inequalities:
$(1) \frac{\sqrt{3}}{3} + \tan x \geq 0$;
$(2) \tan x - \sqrt{3} \leq 0$.

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