
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 function $f(x) = x^2 - 4x + 6$,

(1) If $f(x)$ is monotonically decreasing in the interval $[m, m+1]$, find the range of the real number $m$.

(2) If the minimum value of $f(x)$ in the interval $[a, b]$ ($a < b$) is $a$, and the maximum value is $b$, find the values of $a$ and $b$.

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