
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 rules of a golden egg smashing game are as follows: Each game requires smashing three golden eggs, and each time you smash an egg, it either reveals a golden flower or it doesn't. It is known that the probability of revealing a golden flower each time you smash an egg is $\dfrac{1}{2}$, and the outcomes of smashing eggs are independent of each other. Then, the probability of revealing at least one golden flower in three games is __.

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