
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 $f(x)=\sin ωx (ω > 0)$.
(1) When $ω=1$, write the function expression corresponding to the graph obtained by shifting the graph of $y=f(x)$ to the right by $\frac{π}{6}$ units.
(2) If the graph of $y=f(x)$ passes through the point $(\frac{2π}{3},0)$ and is an increasing function in the interval $(0,\frac{π}{3})$, find the value of $ω$.

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