
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
There are  $100$  people in a room. Some are *wise* and some are *optimists*. $\quad \bullet~$  A *wise* person can look at someone and know if they are wise or if they are an optimist. $\quad \bullet~$  An *optimist* thinks everyone is wise (including themselves).

Everyone in the room writes down what they think is the number of wise people in the room. What is the smallest possible value for the average?  $$ \mathrm a. ~ 10\qquad \mathrm b.~25\qquad \mathrm c. ~50 \qquad \mathrm d. ~75 \qquad \mathrm e. ~100 $$  

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