
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
Mr. Thompson recorded this information from a test taken by his $120$ students. A bonus of $5\%$ was awarded to the students who scored below $60\%$, which raised their score by $5\%$ points but didn't exceed $60\%$. Using the data, calculate the new average percent score for these students:

\begin{tabular}{|c|c|}
\multicolumn{2}{c}{}\\\hline
\textbf{$\%$ Score}&\textbf{Number of Students}\\\hline
100&10\\\hline
90&20\\\hline
80&40\\\hline
70&30\\\hline
60&10\\\hline
50&5\\\hline
40&3\\\hline
30&2\\\hline
\end{tabular}

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