
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
If $x,y>0, \log_y(x)+\log_x(y)=4 \text{ and } xy=64,\text{ then }\frac{x+y}{2}=$
A) $6$
B) $9$
C) $\frac{64^{3/(5+\sqrt{3})} + 64^{1/(5+\sqrt{3})}}{2}$
D) $28$

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