
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
In a 1000-meter race, an hourglass starts leaking sand at a constant rate after a certain period since the race begins. Xiaoming runs at a constant speed. When he reaches 200 meters, the $\mathrm{a}_{\text{th}}$ grain of sand falls into a cup. When he reaches 300 meters, the $\overline{\mathrm{bc}}_{\text{th}}$ grain of sand falls into the cup. When he reaches 400 meters, the $\overline{\mathrm{de}}_{\text{th}}$ grain of sand falls into the cup. When he reaches 500 meters, the $\overline{\mathrm{fg}}_{\text{th}}$ grain of sand falls into the cup.

Given the conditions:
1. $\mathrm{a}$ is a multiple of 2.
2. $\overline{\mathrm{bc}}$ is a prime number.
3. $\overline{\mathrm{de}}$ is a multiple of 5.
4. $\overline{\mathrm{fg}}$ is a multiple of 3.

What are the possible values for the four-digit number $\overline{\mathrm{debc}}$? Write all possible solutions as answers.

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