
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
Let \( a \) be a real number. If there exists a real number \( t \) such that \( \frac{a - \mathrm{i}}{t - \mathrm{i}} + \mathrm{i} \) is real (\( \mathrm{i} \) is the imaginary unit), then what is the range of \( a \)?

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