
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
To transmit a positive integer less than 2000, the Extended Networked Number Node offers three options.

Option 1. Pay $\$$d^2 to send each digit d. For example, 987 would cost $\$$9^2 + $\$$8^2 + $\$$7^2 = $\$$81 + $\$$64 + $\$$49 = $\$$194 to transmit.

Option 2. Encode the integer into binary (base 2) first, and then pay $\$$d to send each digit d. For example, 987 becomes 1111011011 and would cost $\$$1 + $\$$1 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$1 = $\$$8.

Option 3. Encode the integer into hexadecimal (base 16) first, and then pay the sum of the digits in the hexadecimal number. For example, 987 in hexadecimal is 3DB, and the cost would be 3 + 13 + 11 = $\$$27.

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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