
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 total of $100$ is split into four parts proportional to $1$, $3$, $4$, and $6$. After allocating these parts, an extra $12$ is added to the part proportional to $1$. What is this adjusted smallest part?
A) $12$
B) $19\frac{1}{7}$
C) $25$
D) $34$
E) $18\frac{1}{7}$

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