
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 $f(t) = \log_{2}(2-t) + \sqrt{t-1}$ with domain $D$.
(I) Find the domain $D$;
(II) If the function $g(x) = x^{2} + 2mx - m^{2}$ has a minimum value of $2$ on $D$, find the value of the real number $m$.

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