
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
Vasya wants to place numbers from 1 to 6 (each number exactly once) into squares in such a way that the following condition is met: if two squares are connected, then the number in the higher square is greater. How many ways can this be done?

![Diagram](https://cdn.mathpix.com/cropped/2024_05_06_4984b677816e04f7f1c9g-12.jpg?height=357&width=418&top_left_y=548&top_left_x=518)

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