
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
Calculate the following expressions (required to write out necessary steps):
$(1) (316)^{\frac{3}{2}} - (\frac{1}{e})^{\ln 2} - \log_{3} 27$;
$(2)$ Given $2^{a}=3$, express $\log_{4} 18 - \log_{3} 12$ in terms of $a$.

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