
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 group of  $6$  friends are to be seated in the back row of an otherwise empty movie theater with  $8$  seats in a row. Euler and Gauss are best friends and must sit next to each other with no empty seat between them, while Lagrange cannot sit in an adjacent seat to either Euler or Gauss. Calculate the number of different ways the  $6$  friends can be seated in the back row.

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