
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
The number 119 has the following properties:

(a) Division by 2 leaves a remainder of 1;

(b) Division by 3 leaves a remainder of 2;

(c) Division by 4 leaves a remainder of 3;

(d) Division by 5 leaves a remainder of 4;

(e) Division by 6 leaves a remainder of 5.

How many positive integers less than 2007 satisfy these properties?

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