
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 offers two options.

Option 1: Pay $\$$d to send each digit d in decimal form. For example, 487 would cost $\$$4 + $\$$8 + $\$$7 = $\$$19 to transmit.

Option 2: Encode the integer into base 3 first, and then pay $\$$d to send each digit d. For example, 487 becomes 200112 in base 3, and would cost $\$$2 + $\$$0 + $\$$0 + $\$$1 + $\$$1 + $\$$2 = $\$$6.

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}
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