
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 $f(x)=\sin ωx (ω > 0)$, its graph is translated to the right by $\frac{π}{4}$ units to obtain the graph of function $g(x)$. If for the $x_1$ and $x_2$ that satisfy $|f(x_1)-g(x_2)|=2$, we have $|x_1-x_2|_{min}=\frac{π}{4}$, then the value of $f(\frac{π}{4})$ is \_\_\_\_\_\_.

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