
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
Fix a sequence  $ a_1,a_2,a_3,... $  of integers satisfying the following condition:for all prime numbers  $ p $  and all positive integers  $ k $ , we have  $ a_{pk+1}=pa_k-3a_p+13 $ .Determine all possible values of  $ a_{2013} $ .

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