
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 the sequence $\{a\_n\}$ satisfying $a\_1=2$, $a\_2=6$, and $a_{n+2} - 2a_{n+1} + a_n = 2$, using $[x]$ to represent the largest integer not exceeding $x$, such as $[0.6] = 0$, $[1.2] = 1$, find the value of $\left[ \frac{m}{a\_1} + \frac{m}{a\_2} + \ldots + \frac{m}{a\_m} \right]$ in terms of $m$.

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