
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 5000, the Networked Number Node offers two options.

Option 1. Pay $\$$d^2 to send each digit $d$. For instance, 3487 would cost $\$$3^2 + $\$$4^2 + $\$$8^2 + $\$$7^2 = \$9 + \$16 + \$64 + \$49 = \$138 to transmit.

Option 2. Encode the integer into binary (base 2) first, and then pay $\$$d^2 to send each digit $d$. Therefore, 3487 becomes 110110011111 and would cost $\$$1^2 + $\$$1^2 + $\$$0^2 + $\$$1^2 + $\$$1^2 + $\$$0^2 + $\$$0^2 + $\$$1^2 + $\$$1^2 + $\$$1^2 + $\$$1^2 + $\$$1^2 = \$8.

What is the largest integer less than 5000 that costs the same whether using Option 1 or Option 2?

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