
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 $f(x)=x+ \frac{1}{x}$, and $g(x)=f^{2}(x)-af(x)+2a$ has four distinct zeros $x\_1$, $x\_2$, $x\_3$, $x\_4$, determine the value of $[2-f(x\_1)]\cdot[2-f(x\_2)]\cdot[2-f(x\_3)]\cdot[2-f(x\_4)]$.

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