
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 from $2 \times 1$ dominoes in the following way. First, we arrange 55 dominoes to cover a $10 \times 11$ rectangle; this will be the first level of the tower. On top of this, we build additional levels, each containing 55 dominoes, ensuring that every level fits exactly on the previous one. The resulting structure is called stable if every internal grid point of the $10 \times 11$ rectangle is covered by an internal point of a domino on that level. How many levels does the shortest stable tower have?

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