
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 $f(x)=2 \sqrt {3}\sin x\cos x-2\cos ^{2}x+1$.
(I) Find the smallest positive period of the function $f(x)$;
(II) Translate the graph of the function $f(x)$ to the left by $\frac {π}{3}$ units to obtain the graph of function $g(x)$. In $\triangle ABC$, sides $a$, $b$, and $c$ are opposite to angles $A$, $B$, and $C$, respectively. If $g(\frac {A}{2})=1$, $a=2$, and $b+c=4$, find the area of $\triangle ABC$.

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