
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 Networked Number Node has updated its transmission options for positive integers less than 2000.

Option 1. Pay $\$$2d for each digit d in the number. For example, 1987 would cost $\$$2(1 + 9 + 8 + 7) = $\$$50.

Option 2. Encode the integer into binary (base 2) first, and then pay $\$$d for each digit d in the binary form. For example, 1987 becomes 11111000011 in binary and would cost $\$$1 + $\$$1 + $\$$1 + $\$$1 + $\$$1 + $\$$0 + $\$$0 + $\$$0 + $\$$0 + $\$$1 + $\$$1 = $\$$7.

What is the largest integer less than 2000 that costs the same whether using Option 1 or Option 2?

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