
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 definition \\( \begin{pmatrix} a\_1 & a\_2 \\\\ a\_3 & a\_4 \end{pmatrix} = a\_1 a\_4 - a\_2 a\_3 \\), if \\( f(x) = \begin{pmatrix} \sin (\pi - x) & \sqrt{3} \\\\ \cos (\pi + x) & 1 \end{pmatrix} \\), determine the function obtained by shifting the graph of \\( f(x) \\) to the right by \\( \frac{\pi}{3} \\) units.

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