
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 $f(x)=2\cos ( \frac {π}{2}-ωx)+2\sin ( \frac {π}{3}-ωx)(ω > 0,x∈R)$, if $f( \frac {π}{6})+f( \frac {π}{2})=0$, and $f(x)$ is decreasing on the interval $( \frac {π}{6}, \frac {π}{2})$.
(1) Find the value of $f(0)$;
(2) Find the value of $ω$;
(3) Solve the inequality $f(x)\geqslant 1$.

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