
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
Given that the sum of the coefficients of the expansion of $\left( \frac{3}{ \sqrt{a}}- \sqrt[3]{a} \right)^{n}$ is equal to the constant term in the expansion of $\left( 4 \sqrt[3]{b}- \frac{1}{ \sqrt{5b}} \right)^{5}$, find:

$(1)$ The sum of the binomial coefficients in the expansion;

$(2)$ The binomial coefficient of the term containing $a^{-1}$ in the expansion.

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