
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  $f(x) =x^4+14x^3+52x^2+56x+16.$   Let  $z_1, z_2, z_3, z_4$  be the four roots of  $f$ .  Find the smallest possible value of  $|z_az_b+z_cz_d|$  where  $\{a,b,c,d\}=\{1,2,3,4\}$ .

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