
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 $a=2\int_{-3}^{3}{\left( x+\left| x \right| \right)dx}$, determine the total number of terms in the expansion of $\left( \sqrt{x}-\frac{1}{\sqrt[3]{x}} \right)^{a}$ where the power of $x$ is not an integer.

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