
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) = $\overrightarrow {a}$ • ($\overrightarrow {b}$ + $\overrightarrow {c}$), where vector $\overrightarrow {a}$ = (sinx, -cosx), $\overrightarrow {b}$ = (sinx, -3cosx), $\overrightarrow {c}$ = (-cosx, sinx), and x ∈ R.
(1) If f(α) = $\frac{5}{2}$, and $- \frac{5π}{8}$ < α < $- \frac{π}{8}$, find the value of cos2α.
(2) Find the range of real number m such that the inequality |f(x) - m| < 2 holds true for x ∈ [$\frac{π}{8}$, $\frac{π}{2}$].

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