
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
Alice and Bob want to play a game. In the beginning of the game, they are teleported to two random position on a train, whose length is  $ 1 $  km. This train is closed and dark. So they dont know where they are.

Fortunately, both of them have iPhone 133, it displays some information:
1. Your facing direction
2. Your total walking distance
3. whether you are at the front of the train 
4. whether you are at the end of the train 
Moreover, one may see the information of the other one. Once Alice and Bob meet, the game ends. 

Alice and Bob can only discuss their strategy before the game starts. Find the least value  $ x $  so that they are guarantee to end the game with total walking distance  $ \le x $  km.

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