
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
A box contains gold coins. If the coins are equally divided among 8 people, 7 coins are left over. If the coins are equally divided among 7 people, 5 coins are left over. Determine the smallest number of coins in the box that satisfies both conditions. Then find how many coins are left if these coins are divided evenly among 9 people.

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