
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
 $ m$  and  $ n$  are positive integers. In a  $ 8 \times 8$  chessboard,  $ (m,n)$  denotes the number of grids a Horse can jump in a chessboard ( $ m$  horizontal  $ n$  vertical or  $ n$  horizontal  $ m$  vertical ). If a  $ (m,n) \textbf{Horse}$  starts from one grid, passes every grid once and only once, then we call this kind of Horse jump route a  $ \textbf{H Route}$ . For example, the  $ (1,2) \textbf{Horse}$  has its  $ \textbf{H Route}$ . Find the smallest positive integer  $ t$ , such that from any grid of the chessboard, the  $ (t,t\plus{}1) \textbf{Horse}$  does not has any  $ \textbf{H Route}$ .

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