
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
Let  $A$  be the greatest possible value of a product of positive integers that sums to  $2014$ .  Compute the sum of all bases and exponents in the prime factorization of  $A$ .  For example, if  $A=7\cdot 11^5$ , the answer would be  $7+11+5=23$ .

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