
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 robot is standing on the bottom left vertex  $(0,0)$  of a  $5\times5$  grid, and wants to go to  $(5,5)$ , only moving to the right  $(a,b)\mapsto(a+1,b)$  or upward  $(a,b)\mapsto(a,b+1)$ . However this robot is not programmed perfectly, and sometimes takes the upper-left diagonal path  $(a,b)\mapsto(a-1,b+1)$ . As the grid is surrounded by walls, the robot cannot go outside the region  $0\leq a,b\leq5$ . Supposing that the robot takes the diagonal path exactly once, compute the number of different routes the robot can take.

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