
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
The Networked Number Node has extended its service to transmit a positive integer less than 5000. The costing options have also been revised.

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

Option 2. Encode the integer into binary (base 2) first, and then pay $\$$d to transmit each binary digit d. For example, 987 becomes 1111011011, costing $\$$1 + $\$$1 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$1 = $\$$8.

Find the smallest prime number less than 5000 that costs less to transmit using Option 2 than with Option 1.

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