
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
First, translate the graph of the function $y=\cos x$ by moving it $\frac{\pi}{3}$ units to the right, then shorten the abscissa of the obtained points to $\frac{1}{2}$ of the original length (the ordinate remains unchanged). Find the analytical expression of the resulting function graph.

A) $y=\cos (2x+\frac{\pi}{3})$
B) $y=\cos (2x-\frac{\pi}{3})$
C) $y=\cos (\frac{1}{2}x+\frac{\pi}{3})$
D) $y=\cos (\frac{1}{2}x-\frac{\pi}{3})$

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