
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
A finite sequence of positive integers  $ m_i$  for  $ i\equal{}1,2,...,2006$  are defined so that  $ m_1\equal{}1$  and  $ m_i\equal{}10m_{i\minus{}1} \plus{}1$  for  $ i>1$ . How many of these integers are divisible by  $ 37$ ?

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