
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 $$\overrightarrow {m} = (2-\sin(2x+ \frac {\pi}{6}), -2)$$, $$\overrightarrow {n} = (1, \sin^2x)$$, $f(x) = \overrightarrow {m} \cdot \overrightarrow {n}$, where $x \in [0, \frac {\pi}{2}]$

(1) Find the range of the function $f(x)$.

(2) Suppose $\triangle ABC$ has internal angles $A$, $B$, $C$ with opposite sides of lengths $a$, $b$, $c$ respectively. If $f(\frac {B}{2}) = 1$, $b = 1$, and $c = \sqrt {3}$, find the value of $a$.

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