
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 $M$ be the number of ways to write $5030$ as $5030 = b_3 \cdot 10^3 + b_2 \cdot 10^2 + b_1 \cdot 10 + b_0$, where $b_i$'s are even integers, and $0 \le b_i \le 98$. Find $M$.

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