
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
Sort the following fractions in ascending order:

$$
t_{1}=\frac{100^{100}+1}{100^{90}+1}, \quad t_{2}=\frac{100^{99}+1}{100^{89}+1}, \quad t_{3}=\frac{100^{101}+1}{100^{91}+1}, \quad t_{4}=\frac{101^{101}+1}{101^{91}+1}, \quad t_{5}=\frac{101^{100}+1}{101^{90}+1}, \quad t_{6}=\frac{99^{99}+1}{99^{89}+1}, \quad t_{7}=\frac{99^{100}+1}{99^{90}+1}
$$

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