
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
There are more than 5000 toothpicks, which can be divided into small packs of six different specifications. If packed 10 toothpicks per pack, 9 toothpicks will remain in the end. If packed 9 toothpicks per pack, 8 toothpicks will remain. For the third, fourth, fifth, and sixth specifications, if packed 8, 7, 6, and 5 toothpicks per pack, respectively, 7, 6, 5, and 4 toothpicks will remain. How many toothpicks were there originally?

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