
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
At the turn of the 16th and 17th centuries, with the development of astronomy, navigation, engineering, trade, and military, improving numerical calculation methods became urgent. John Napier invented logarithms to simplify calculations in the process of studying astronomy. Later, the genius mathematician Euler discovered the relationship between logarithms and exponents, that is, $a^{b}=N \Leftrightarrow b=\log_{a}N$. Given $2^{a}=6$ and $3^{b}=36$, find $\frac{{4^a}}{{9^b}}$ and $\frac{1}{a}+\frac{2}{b}$.

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