
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 $f(x) = \sin(\omega x + \varphi)$ $(ω > 0, -\frac{π}{2} < \varphi < \frac{π}{2})$, each point's abscissa on its graph is shortened to half of the original length, while the ordinate remains unchanged. Then, the graph is shifted to the right by $\frac{π}{6}$ units to obtain the graph of $g(x) = \sin x$. Determine the value of $f(\frac{π}{3})$.

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