
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
Find all sets of three positive integers \((I, M, C)\) (where \(I\), \(M\), and \(C\) are prime numbers and \(I \leq M \leq C\)) such that
\[I \cdot M \cdot C = I + M + C + 1007.\]

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