
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 Enhanced Number Nodal Network (ENNN) has two transmission options:

Option 1. Pay $\$$2d for sending each even digit d and $\$$d for each odd digit d. For example, 486 costs $\$$2×4 + $\$$8 + $\$$2×6 = $\$$8 + $\$$8 + $\$$12 = $\$$28.

Option 2. Encode the integer into binary (base 2) first, then pay $\$$2 for every '1' and $\$$1 for every '0' in the binary representation. For example, 486 becomes 111100110 and costs $\$$2×6 + $\$$1×3 = $\$$12 + $\$$3 = $\$$15.

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