
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  $a$  and  $b$  be positive integers such that the number  $b^2 + (b +1)^2 +...+ (b + a)^2-3$  is multiple of  $5$  and  $a + b$  is odd. Calculate the digit of the units of the number  $a + b$  written in decimal notation.

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