
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
If a sequence $\{a_n\}$ satisfies: $a_1 < a_2 > a_3 < a_4 > \ldots > a_{2n-1} < a_{2n} > \ldots$, then the sequence $\{a_n\}$ is called a "sine sequence". Now, arrange the numbers $1$, $2$, $3$, $4$, $5$ into a "sine sequence". Let the total number of such arrangements be $a$. Then, the coefficient of the $x^2$ term in the expansion of $(\sqrt{x} - \frac{a}{\sqrt{x}})^6$ is ______.

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