
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
Huanhuan and Lele are playing a game together. In the first round, they both gain the same amount of gold coins, and in the second round, they again gain the same amount of gold coins. 

At the beginning, Huanhuan says: "The number of my gold coins is 7 times the number of your gold coins."

At the end of the first round, Lele says: "The number of your gold coins is 6 times the number of my gold coins now."

At the end of the second round, Huanhuan says: "The number of my gold coins is 5 times the number of your gold coins now."

Find the minimum number of gold coins Huanhuan had at the beginning.

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