
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
A real number estate is forming three representative teams to participate in the "Sports Carnival" event. Please carefully identify the following "number players": $0$, $-8$, $\sqrt{13}$, $\frac{1}{7}$, $\pi$, $0.505$, and place them in their respective teams.<br/>Integer team: $\{ \_\_\_\_\_\_\}$;<br/>Fraction team: $\{ \_\_\_\_\_\_\}$;<br/>Irrational number team: $\{ \_\_\_\_\_\_\}$.

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