
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
Let $g(x)=x^4+10x^3+35x^2+50x+24$. Let $w_1, w_2, w_3, w_4$ be the four roots of $g$. Find the smallest possible value of $|w_{a}w_{b}+w_{c}w_{d}|$ where $\{a,b,c,d\}=\{1,2,3,4\}$.

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