
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
Starting with a positive integer  $M$  written on the board , Alice plays the following game: in each move, if  $x$  is the number on the board, she replaces it with  $3x+2$ .Similarly, starting with a positive integer  $N$  written on the board, Bob plays the following game: in each move, if  $x$  is the number on the board, he replaces it with  $2x+27$ .Given that Alice and Bob reach the same number after  playing  $4$  moves each, find the smallest value of  $M+N$ 

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