
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 that function f(x) is an increasing function on R and f(sinω) + f(-cosω) > f(cosω) + f(-sinω), where ω is an acute angle, and function g(x) = sin(ωx + $\frac{π}{4}$) is monotonically decreasing in the interval ($\frac{π}{2}$, π), determine the range of ω.

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