
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
In English class, you have discovered a mysterious phenomenon -- if you spend  $n$  hours on an essay, your score on the essay will be  $100\left( 1-4^{-n} \right)$  points if  $2n$  is an integer, and  $0$  otherwise. For example, if you spend  $30$  minutes on an essay you will get a score of  $50$ , but if you spend  $35$  minutes on the essay you somehow do not earn any points.

It is 4AM, your English class starts at 8:05AM the same day, and you have four essays due at the start of class. If you can only work on one essay at a time, what is the maximum possible average of your essay scores?

*Proposed by Evan Chen*

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