
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 Enhanced Networked Number Service transmits a positive integer less than 2000 with two payment options:
Option 1: Pay $\$(d+2)$ to send each digit d in the integer. For a number like 1234, the cost would be $\$$(1+2) + \$(2+2) + \$(3+2) + \$(4+2) = \$14$.
Option 2: Convert the integer to binary first, and then pay $\$(d+2)$ for each digit d. For instance, for 1234, in binary is 10011010010, the cost would be $\$(1+2) + \$(0+2) + \$(0+2) + \$(1+2) + \$(1+2) + \$(0+2) + \$(1+2) + \$(0+2) + \$(0+2) + \$(1+2) + \$(0+2) = \$22$.
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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