
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  $A(x)=\lfloor\frac{x^2-20x+16}{4}\rfloor$ ,  $B(x)=\sin\left(e^{\cos\sqrt{x^2+2x+2}}\right)$ ,  $C(x)=x^3-6x^2+5x+15$ ,  $H(x)=x^4+2x^3+3x^2+4x+5$ ,  $M(x)=\frac{x}{2}-2\lfloor\frac{x}{2}\rfloor+\frac{x}{2^2}+\frac{x}{2^3}+\frac{x}{2^4}+\ldots$ ,  $N(x)=\textrm{the number of integers that divide }\left\lfloor x\right\rfloor$ ,  $O(x)=|x|\log |x|\log\log |x|$ ,  $T(x)=\sum_{n=1}^{\infty}\frac{n^x}{\left(n!\right)^3}$ , and  $Z(x)=\frac{x^{21}}{2016+20x^{16}+16x^{20}}$  for any real number  $x$  such that the functions are defined. Determine   $$ C(C(A(M(A(T(H(B(O(N(A(N(Z(A(2016)))))))))))))). $$  *2016 CCA Math Bonanza Lightning #5.3*

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