
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
Certain bacteria split once every two hours (each bacterium splits into two, ignoring the time required for splitting). At the beginning of the research, there are two bacteria. During the research, the bacteria continuously split. The total number of bacteria, $y$, is a function of the research time, $t$, denoted as $y=f(t)$.
(1) Write the domain and range of the function $y=f(t)$.
(2) Draw the graph of $y=f(t)(0 \leqslant t<6)$ in the given coordinate system.
(3) Write the expression for the total number of bacteria at $n$ hours $(n \geqslant 0, n \in \mathbf{Z})$.

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