
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
Let \(f(x) = \sin{x} + 2\cos{x} + 2\tan{x}\), using radian measure for the variable \(x\). Find the smallest positive value of \(x\) for which \(f(x) = 0\), and denote this value as \(r\). Calculate \(\lfloor r \rfloor\).

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