
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 it splits into two amoebas the next day. From the second day onward, every amoeba that was born the previous day splits into two new amoebas. After one week, how many amoebas are in the puddle? Assume the puddle has no amoebas before the first one is placed and there are no external influences on the amoeba population.

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