
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 $\overrightarrow {m}$=(2sinωx, 2cosωx) and $\overrightarrow {n}$=(1, 1), where ω > 0, let function f(x) be the projection of vector $\overrightarrow {m}$ onto vector $\overrightarrow {n}$. Additionally, x = $\frac {π}{4}$ is the symmetric axis of the graph of function f(x) that is closest to the y-axis.
(I) Find the expression for function f(x).
(II) If cosθ = $\frac {4}{5}$, where θ ∈ ($\frac {3π}{2}$, 2π), find the value of f($θ+ \frac {π}{12}$).

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