
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 that $M$ and $N$ are points on the sides $BC$ and $CA$ of $\triangle ABC$, respectively, and $\overrightarrow{BM} = \frac{1}{3}\overrightarrow{BC}$, $\overrightarrow{CN} = \frac{1}{3}\overrightarrow{CA}$. If $\overrightarrow{AB} = \overrightarrow{a}$ and $\overrightarrow{AC} = \overrightarrow{b}$, and $\overrightarrow{MN} = r\overrightarrow{a} + s\overrightarrow{b}$, calculate the value of $r - s$.

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