
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 of a $2×2$ matrix as $\begin{vmatrix} a_{1} & a_{2} \\ a_{3} & a_{4} \end{vmatrix}=a_{1}a_{4}-a_{2}a_{3}$, determine the equation of the tangent line to the graph of the function $f(x)=\begin{pmatrix} x^{2}-x & 1 \\ x & \frac{x}{3} \end{pmatrix}$ at the point $(1,-1)$.

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