
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 vectors $\overrightarrow {m}=(2\cos x, \sin x)$ and $\overrightarrow {n}=(\cos x, 2 \sqrt {3} \cos x)$, where $x \in \mathbb{R}$, define the function $f(x) = \overrightarrow {m} \cdot \overrightarrow {n} - 1$.

1. Find the value of $f(\frac{\pi}{6})$.
2. Find the interval(s) where the function $f(x)$ is strictly increasing.

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