
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 sequence $\{a_n\}$ satisfying $a_1 = 2$, $a_2 = 6$, and $a_{n+2} - 2a_{n+1} + a_n = 2$, let $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$ (e.g., $\lfloor 0.6 \rfloor = 0$, $\lfloor 1.2 \rfloor = 1$). Then, the value of
$$\left\lfloor \frac{m}{a_1} + \frac{m}{a_2} + \ldots + \frac{m}{a_m} \right\rfloor$$
expressed in terms of $m$ is __________.

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