
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
Define $$\begin{pmatrix} a_{1} & a_{2} \\ a_{3} & a_{4}\end{pmatrix}$$ as $a_{1}a_{4} - a_{2}a_{3}$. If $f(x) = \begin{pmatrix} \sin(\pi-x) & \sqrt{3} \\ \cos(\pi+x) & 1\end{pmatrix}$, find the equation of 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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