
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
Consider the function $f(x) = x^2 - 2x + 2$ defined on the closed interval $[t, t+1]$ (where $t \in \mathbb{R}$). Let $g(t)$ represent the minimum value of $f(x)$ on this interval.
1. Write down the expression for $g(t)$.
2. Sketch the graph of $g(t)$ and determine its minimum value.

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