
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 $f(x)= \sqrt{2}\sin \left( \left. ωx- \dfrac{π}{4} \right. \right)(ω > 0)$ with the smallest positive period of $π$.

(1) Find the value of $ω$;

(2) If $x∈\left[\left. 0, \dfrac{π}{2} \right. \right]$ and $f(x)=0$, find the value of $x$.

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