
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 function $f(x) = x^2 - 4x - 4$ has its minimum value on the interval $[t, t+1]$ (where $t \in \mathbb{R}$) denoted as $g(t)$.  
(1) Write the expression for the function $g(x)$.  
(2) Find the minimum value of $g(t)$.

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