
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
(The full score of this question is 12 points)

The function $f(x) = x^2 - 2x + 2$ has a minimum value on the closed interval $[t, t+1]$ ($t \in \mathbb{R}$), which is denoted as $g(t)$.

(1) Please write down the expression for $g(t)$.

(2) Draw the graph of $g(t)$ and write down the minimum value of $g(t)$.

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