
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 500, the Networked Number Node has revised its payment options.

Option 1. Pay $\$$d to send each digit d. For example, 234 would cost $\$$2 + $\$$3 + $\$$4 = $\$$9 to transmit.

Option 2. Encode the integer into binary (base 2) first, and then pay $\$$2 for each '1' and $\$$1 for each '0'. For example, 234 becomes 11101010 in binary and would cost $\$$2 + $\$$2 + $\$$2 + $\$$1 + $\$$1 + $\$$2 + $\$$1 + $\$$1 = $\$$12.

What is the largest integer less than 500 that costs the same whether using Option 1 or Option 2?

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