
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 first term of an arithmetic sequence \\({a\_n}\\) is \\(a\_1=C_{5m}^{11-2m}-A_{11-3m}^{2m-2}\\) (where \\(m \in \mathbb{N}\\)), and the common difference is the constant term in the expansion of \\((\frac{5}{2x}-\frac{2}{5}\sqrt[3]{x^{2}})^{n}\\), where \\(n\\) is the remainder when \\(77^{77}-15\\) is divided by \\(19\\), find the general term \\(a\_n\\).

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