
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 quadratic function $f(x) = x^2 - 2x + 3$,
(I) If the minimum value of the function $y = f(\log_{3}x + m)$, where $x \in [\frac{1}{3}, 3]$ is 3, find the value of the real number $m$;
(II) If for any two distinct $x_1, x_2 \in (2, 4)$, the inequality $|f(x_1) - f(x_2)| < k|x_1 - x_2|$ holds, find the range of the real number $k$.

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