
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
Consider the polynomials  $P\left(x\right)=16x^4+40x^3+41x^2+20x+16$  and  $Q\left(x\right)=4x^2+5x+2$ . If  $a$  is a real number, what is the smallest possible value of  $\frac{P\left(a\right)}{Q\left(a\right)}$ ?

*2016 CCA Math Bonanza Team #6*

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