
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 99 people participated in a math competition, which was divided into three sections: geometry, number theory, and combinatorics. Xiao Ming ranked 16th in the number theory exam, 30th in the combinatorics exam, and 23rd in the geometry exam. Xiao Ming did not tie with anyone in any of the exams. The final overall ranking is determined by summing the scores of the three exams and then ranking from high to low. If we use the rank $\mathrm{A}$ to represent the best possible overall ranking Xiao Ming could achieve (the smaller the $\mathrm{A}$, the better the ranking), and the rank $\mathrm{B}$ to represent the worst possible overall ranking Xiao Ming could achieve, then $100 \cdot A + B = (\quad)$.

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