
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
Let \\(\lfloor x \rfloor\\) denote the greatest integer less than or equal to \\(x\\), such as \\(\lfloor 0.78 \rfloor = 0\\), \\(\lfloor 3.01 \rfloor = 3\\). If the sequence \\(\{x_n\}\\) is defined by the formula \\(x_n = \left\lfloor \frac{n}{5} \right\rfloor (n \in \mathbb{N}^*)\\), then the sum \\(x_1 + x_2 + \ldots + x_{5n} =\\) \_\_\_\_\_\_.

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