
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
a) Find all solutions to the system of equations (1)-(3). Additionally, provide one example of a system of equations that differs from the given system by exactly one coefficient and

b) has infinitely many solutions,

c) is not satisfied by any real number triplet $x, y, z$.

$$
\begin{gathered}
2x + 3y + z = 1 \\
4x - y + 2z = 2 \\
8x + 5y + 3z = 4
\end{gathered}
$$

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