
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 $\overrightarrow {m}$=(cosx, sinx) and $\overrightarrow {n}$=(cosx, $\sqrt {3}$cosx), where x∈R, define the function f(x) = $\overrightarrow {m}$$\cdot \overrightarrow {n}$+ $\frac {1}{2}$.
(1) Find the analytical expression and the interval where the function is strictly increasing;
(2) Let a, b, and c be the sides opposite to angles A, B, and C of △ABC, respectively. If f(A)=2, b+c=$2 \sqrt {2}$, and the area of △ABC is $\frac {1}{2}$, find the value of a.

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