
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 1000, the Networked Number Node provides two options.

Option 1. Pay $\$$d to send each digit d. For instance, the number 987 would cost $\$$9 + $\$$8 + $\$$7 = $\$$24 to transmit.

Option 2. Encode the integer into ternary (base 3) first, and then pay $\$$d to send each digit d. For example, 987 converts to 1100200 in ternary and would cost $\$$1 + $\$$1 + $\$$0 + $\$$0 + $\$$2 + $\$$0 + $\$$0 = $\$$4.

What is the largest integer less than 1000 that costs the same using Option 1 or Option 2 in this configuration?

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