
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
Given that the heights of 6 cacti are integers and each cactus is either twice as tall, the same height, or half as tall as the one to its right, reconstruct the sequence of the heights of the cacti, and calculate the average height in meters.

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