
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 $M$ be the positive integer $555\ldots555$, a $303$-digit number where each digit is a $5$. Let $g(r)$ be the leading digit of the $r$th root of $M$. Calculate the sum of $g(2)$, $g(3)$, $g(4)$, $g(5)$, and $g(6)$.

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