
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
 We say that a natural number  $n$  is interesting if it can be written in the form 

       \[
 n = \left\lfloor \frac{1}{a} \right\rfloor + \left\lfloor \frac{1}{b} \right\rfloor + \left\lfloor \frac{1}{c} \right\rfloor,
 \] where  $a,b,c$  are positive real numbers such that  $a + b + c = 1.$  Determine all interesting numbers. (  $\lfloor x \rfloor$  denotes the greatest integer not greater than  $x$ .)

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