
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
An amoeba is placed in a puddle one day, and on that same day, it splits into two amoebas with a probability of 0.8. Each subsequent day, every amoeba in the puddle has a probability of 0.8 to split into two new amoebas. After one week, assuming no amoebas die, how many amoebas are there in the puddle on average? (Assume the puddle had no amoebas before the first one was placed in it.)

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