
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
$e$ is a mathematical constant, defined as $e=\lim_{x→∞}{({1+\frac{1}{x}})^x}$. Its numerical value is approximately $2.7182818284\ldots$. Zixuan plans to create a password for his phone by rearranging the first $5$ digits of $e$: $2$, $7$, $1$, $8$, $2$. If he wants to ensure that the two $2$s are not adjacent, how many different passwords can Zixuan create? (Answer in numerical form).

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