
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
In the domain of real numbers, consider the equation in \( x \):
\[ 
3x + 7t - 2 + \frac{2tx^2 + 7t^2 - 9}{x - t} = 0 
\]

It has exactly one real root. Find the value of the real number \( t \).

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