
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
Given that $R(n)$ is the sum of the remainders when $n$ is divided by $2$, $3$, ..., and $12$, and $S(n)$ is the digit sum of $n$, find all two-digit numbers such that $R(n) = R(n+1)$ and $S(n)$ is even.

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