
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 binomial coefficients of the first three terms of ${(ax-\frac{1}{\sqrt{x}})}^{n}$ expansion is $22$, and the sum of all coefficients is $1$.<br/>$(1)$ Find the values of $n$ and $a$;<br/>$(2)$ Determine if there is a constant term in the expansion. If there is, find the constant term; if not, explain why.

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