
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
Given an  $m\times n$  grid with unit squares coloured either black or white, a black square in the grid is *stranded*if there is some square to its left in the same row that is white and there is some square above it in the same column that is white.
Find a closed formula for the number of  $2\times n$  grids with no stranded black square.
Note that  $n$  is any natural number and the formula must be in terms of  $n$  with no other variables.

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