
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 call a number lucky if it can be expressed as the sum of positive integers whose reciprocals sum to 1. For example, $11 = 2 + 3 + 6$ and $4 = 2 + 2$ are lucky numbers because

$$
\frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1 \quad \text{and} \quad \frac{1}{2} + \frac{1}{2} = 1
$$

Is $2005$ a lucky number?

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