
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
Erick stands in the square in the 2nd row and 2nd column of a 5 by 5 chessboard.  There are \ $1 bills in the top left and bottom right squares, and there are \$ 5 bills in the top right and bottom left squares, as shown below.
\[\begin{tabular}{|p{1em}|p{1em}|p{1em}|p{1em}|p{1em}|}
\hline
\ $1 & & & & \$ 5 
\hline
& E & & &
\hline
& & & &
\hline
& & & &
\hline
\ $5 & & & & \$ 1 
\hline \end{tabular}\]
Every second, Erick randomly chooses a square adjacent to the one he currently stands in (that is, a square sharing an edge with the one he currently stands in) and moves to that square.  When Erick reaches a square with money on it, he takes it and quits.  The expected value of Erick's winnings in dollars is  $m/n$ , where  $m$  and  $n$  are relatively prime positive integers.  Find  $m+n$ .

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