
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
Mrs. Riley revised her data after realizing that there was an additional score bracket and a special bonus score for one of the brackets. Recalculate the average percent score for the $100$ students given the updated table:

\begin{tabular}{|c|c|}
\multicolumn{2}{c}{}\\\hline
\textbf{$\%$ Score}&\textbf{Number of Students}\\\hline
100&5\\\hline
95&12\\\hline
90&20\\\hline
80&30\\\hline
70&20\\\hline
60&8\\\hline
50&4\\\hline
40&1\\\hline
\end{tabular}

Furthermore, all students scoring 95% receive a 5% bonus, which effectively makes their score 100%.

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