
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
A physicist is conducting an experiment involving $n$ sensors. Each sensor records a signal strength. Let the total sum of the signal strengths recorded by all sensors be 500, and the sum of the fourth powers of these strengths be 80000. Determine the smallest number of sensors $n$ for this scenario to be possible.

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