
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 $$f(x)=\sin(2x+ \frac {π}{6})+2\sin^{2}x$$．
(I) Find the smallest positive period and the monotonically decreasing interval of the function $f(x)$;
(II) In $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$, respectively. If $$f( \frac {A}{2})= \frac {3}{2}$$, $b+c=7$, and the area of $\triangle ABC$ is $$2 \sqrt {3}$$, find the length of side $a$.

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