
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
The sum  $\frac{2}{3\cdot 6} +\frac{2\cdot 5}{3\cdot 6\cdot 9} +\ldots +\frac{2\cdot5\cdot \ldots \cdot 2015}{3\cdot 6\cdot 9\cdot \ldots \cdot 2019}$  is written as a decimal number. Find the first digit after the decimal point.

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