
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 $m$ be an integer, and $4 < m < 40$. The equation $x^2 - 2(2m-3)x + 4m^2 - 14m + 8 = 0$ has two distinct integer roots. Find the value of $m$ and the roots of the equation.

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