
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 the graph of the function $y=f\left(x\right)$ is transformed by first compressing its x-coordinates by a factor of $\frac{1}{2}$ and then shifting it to the right by $\frac{π}{3}$ units, resulting in the graph of the function $y=\sin (x-\frac{π}{4})$, determine the function $f\left(x\right)$.

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