
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 function $f(x) = (\frac{1}{3})^x$ and its graph intersects with the line $y = 5 - x$ at horizontal coordinates $x\_1$ and $x\_2$. Additionally, the function $g(x) = \log_{\frac{1}{3}} x$ intersects with the line $y = 5 - x$ at horizontal coordinates $x\_3$ and $x\_4$. Find the value of $x\_1 + x\_2 + x\_3 + x\_4$.

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