
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 a certain type of virus that doubles every $30min$ and follows the growth law $y=e^{kt}$, where $k$ is a constant, $t$ represents time in hours, and $y$ represents the number of viruses.

$(1)$ Find the constant $k$;

$(2)$ How many viruses can $1$ of this type grow into after $5h$?

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