
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 function $$f(x)= \frac {1}{2}cos^{2}x+ \frac { \sqrt {3}}{2}sinxcosx$$, where $x \in \mathbb{R}$.
(1) Find the minimum value of the function $f(x)$ and write the set of $x$ when $f(x)$ reaches its minimum value.
(2) Translate the graph of the function $f(x)$ to the right by $\frac{\pi}{6}$ units to obtain the graph of the function $g(x)$. Find the interval where $g(x)$ is monotonically increasing.

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