
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
The quadratic polynomials \( f(x) \) and \( g(x) \) are such that

\[
\begin{aligned}
& f(2) \\
& g(2)
\end{aligned}=\begin{aligned}
& f(3) \\
& g(3)
\end{aligned}=2
\]

Find \( f(1) \), given that \( g(1) = 2 \), \( f(5) = 7 \), and \( g(5) = 2 \).

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