
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
A number is called *capicua* if when it is written in decimal notation, it can be read equal from left to right as from right to left; for example:  $8, 23432, 6446$ . Let  $x_1<x_2<\cdots<x_i<x_{i+1},\cdots$  be the sequence of all capicua numbers. For each  $i$  define  $y_i=x_{i+1}-x_i$ . How many distinct primes contains the set  $\{y_1,y_2, \ldots\}$ ?

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