
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
We call a sequence of \(n\) digits one or zero a code. A subsequence of a code is a palindrome if it is the same after we reverse the order of its digits. A palindrome is called nice if its digits occur consecutively in the code. For example, the code \(1101\) contains 10 palindromes, of which 6 are nice.

a) What is the least number of palindromes in a code?

b) What is the least number of nice palindromes in a code?

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