
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
The price of a light bulb is \( 8 \) Ft, and its lifespan as a function of the voltage is given by \( E = 2 \cdot 10^6 \cdot 2^{-U/(10 \, \text{V})} \) hours. The efficiency (candle/watt) as a function of the voltage is \( G = 4 \cdot 10^{-5} (U / 1 \, \text{V})^{1.7} \) candle/watt. The price of \( 1 \, \text{kWh} \) of energy is \( 2.1 \) Ft. At what voltage should we operate the light bulb to get the cheapest light on average over a long period? The resistance of the filament is \( R = 200 \, \Omega \); assume it is independent of the voltage.

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