
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
We build a tower of  $2\times 1$  dominoes in the following way. First, we place  $55$  dominoes on the table such that they cover a  $10\times 11$  rectangle; this is the first story of the tower. We then build every new level with  $55$  domioes above the exact same  $10\times 11$  rectangle. The tower is called *stable* if for every non-lattice point of the  $10\times 11$  rectangle, we can find a domino that has an inner point above it. How many stories is the lowest *stable* tower?

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