
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]


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At the beginning of the first year, a shopping mall invested 500,000 yuan in commodity operations, and at the end of each year, the total capital is the sum of the initial capital invested at the beginning of that year. If the annual profit rate for the first year is $P$, determine the algebraic expression for the total capital at the end of the first year in ten thousand yuan.

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