
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
Find all prime numbers  $p$  for which one can find a positive integer  $m$  and nonnegative integers  $a_0,a_1,...,a_m$  less than  $p$  such that   $$ \begin{cases}  a_0+a_1p+...+a_{m-1}p^{m-1}+a_{m}p^{m} = 2013 
 a_0+a_1+...+a_{m-1}+a_{m} = 11\end{cases} $$  

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