
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
Given two functions defined on the real numbers:

\[ 
\begin{aligned}
& f(x)=t x^{2}-x+1 \\
& g(x)=2 t x-1 
\end{aligned}
\]

where \( t \) is a real parameter. How many intersection points do the graphs of \( f \) and \( g \) have?

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