
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
Harry Potter can do any of the three tricks arbitrary number of times: $i)$  switch  $1$  plum and  $1$  pear with  $2$  apples  $ii)$  switch  $1$  pear and  $1$  apple with  $3$  plums  $iii)$  switch  $1$  apple and  $1$  plum with  $4$  pears 
In the beginning, Harry had  $2012$  of plums, apples and pears, each. Harry did some tricks and now he has  $2012$  apples,  $2012$  pears and more than  $2012$  plums. What is the minimal number of plums he can have?

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