
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
Upon entering the atmosphere, an asteroid heated up significantly and exploded as it approached the Earth's surface, breaking into a large number of fragments. Scientists collected all the fragments and divided them into groups based on their size. It was found that one-fifth of all the fragments had a diameter of 1 to 3 meters, another 26 were very large (more than 3 meters in diameter), and the rest were divided into several groups, each consisting of 1/7 of the total number of fragments. What is the total number of fragments collected by the scientists?

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