
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
Mathematics and literature have many fascinating connections, such as palindromic poems in literature like "儿忆父兮妻忆夫" which can be read forwards and backwards, and palindromic numbers in mathematics like $343$ and $12521$. There are $9$ two-digit palindromic numbers: $11$, $22$, $33$, ..., $99$. What is the probability that a three-digit palindromic number is even?

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