
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
Vanya is devising a password for his phone using non-repeating digits with no zeros. The password works in such a way that if, without lifting his finger from the screen, he sequentially connects points corresponding to the digits of the password with line segments, the phone will unlock. However, the phone does not allow connecting two points with a line segment if there is a third point between them: if Vanya connects, for example, 1 and 3, the phone will interpret it as 1-2-3.

Vanya wants the line formed while inputting the password to not intersect itself. Additionally, by rearranging the digits of the password in any order other than the reverse, it should not be possible to create another such line. For example, the password 1263 is not acceptable to Vanya because the line formed by 6-3-2-1 is different but also has no self-intersections. Vanya came up with the password 723. These three digits - 2, 3, and 7 - cannot be connected in any other way to form a different valid line. Unfortunately, this password is quite short.

Help Vanya come up with a longer password. Write the password and draw the unique line that can be formed using these digits.

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