
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
Given a sequence $a_1, a_2, a_3, \ldots a_{100}$, where each term is a positive integer, and there are $k_i$ terms equal to $i$ (for $i=1,2,3,\ldots$), let $b_j = k_1 + k_2 + \ldots + k_j$ (for $j=1,2,3,\ldots$), define $g(m) = b_1 + b_2 + \ldots + b_m - 100m$ (for $m=1,2,3,\ldots$).
(I) Suppose the sequence is defined as $k_1 = 40$, $k_2 = 30$, $k_3 = 20$, $k_4 = 10$, and $k_5 = \ldots = k_{100} = 0$,
   1. Find the values of $g(1), g(2), g(3), g(4)$.
   2. Find the value of the sum $a_1 + a_2 + a_3 + \ldots + a_{100}$.
(II) If the maximum term in $a_1, a_2, a_3, \ldots a_{100}$ is 50, compare the values of $g(m)$ and $g(m+1)$.

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