
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
If a sequence $\left\{a_{1}, a_{2}, \ldots, a_{n}\right\}$ of positive integers (where $n$ is a positive integer) has the property that the last digit of $a_{k}$ is the same as the first digit of $a_{k+1}$ (here $k=1,2, \ldots, n$ and we define $a_{n+1}=a_{1}$), then the sequence is said to be a 'dragon sequence'. For example, $\{414\}$, $\{208, 82\}$, and $\{1, 17, 73, 321\}$ are all 'dragon sequences'. At least how many two-digit numbers must be chosen at random to ensure that a 'dragon sequence' can be formed among some of the chosen numbers?

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