
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
Petya gave Vasya a number puzzle. Petya chose a digit  $X$  and said, "I am thinking of a three digit number that is divisible by 11. The hundreds digit is  $X$  and the tens digit is 3. Find the units digit." Vasya was excited because he knew how to solve this problem, but then realized that the problem Petya gave did not have an answer. What digit  $X$  did Petya chose?

*Ray Li.*

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