
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 $\overrightarrow {a}$ = (cos($\frac {π}{3}$ - x), -sin(x)) and $\overrightarrow {b}$ = (sin(x + $\frac {π}{6}$), sin(x)), and a function f(x) = $\overrightarrow {a}$ • $\overrightarrow {b}$:
(I) Find the smallest positive period and the monotonically decreasing interval of function f(x);
(II) In triangle ABC, if side c opposite angle C is 2$\sqrt {3}$, and f(C) = -$\frac {1}{2}$, find the maximum value of the area of triangle ABC.

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