
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
There is a pile of eggs. Joan counted the eggs, but her count was way off by  $1$  in the  $1$ 's place. Tom counted in the eggs, but his count was off by  $1$  in the  $10$ 's place. Raoul counted the eggs, but his count was off by  $1$  in the  $100$ 's place. Sasha, Jose, Peter, and Morris all counted the eggs and got the correct count. When these seven people added their counts together, the sum was  $3162$ . How many eggs were in the pile?

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