
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 $\lfloor 0.78 \rfloor = 0$, $\lfloor 3.01 \rfloor = 3$. Define the sequence $\{x_n\}$ by the general term $x_n = \left\lfloor \frac{n}{5} \right\rfloor$ (where $n\in\mathbb{N}^+$). Find the sum $x_1 + x_2 + \ldots + x_{5n}$.

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