
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 Networked Number Node offers two options:
Option 1: Pay $\$$d to send each digit d. For example, 1597 would cost $\$$1 + $\$$5 + $\$$9 + $\$$7 = $\$$22 to transmit.
Option 2: Encode the integer into binary (base 2) first and then pay $\$$d to send each digit d, with the additional requirement that the binary number ends in at least two zeros. For example, 1597 becomes 11000110101 and would have to be adjusted to 1100011010100, costing $\$$1 + $\$$1 + $\$$0 + $\$$0 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$0 + $\$$1 + $\$$0 + $\$$0 + $\$$0 = $\$$6.

What is the largest integer less than 2000 that, when transmitted using either option, costs the same amount and is odd?

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