
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
Let's say that a number has the form $\overline{a b a}$ if its first and third digits are the same, and the second digit must be different. For example, 101 and 292 have this form, while 222 and 123 do not. Similarly, define the form of the number $\overline{a b c a b d}$. How many odd numbers of the form $\overline{a b c a b d}$ are divisible by 5?

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