
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
Solve the system of equations (1) - (3) for the values given by sets (4) and (5).

$$
x+a y+a^{2} z=A
$$

$$
x+b y+b^{2} z=B
$$

$$
x+c y+c^{2} z=C
$$

$$
\left\{\begin{array}{l}
A=b+c \\
B=c+a \\
C=a+b
\end{array}\right.
$$

$$
\left\{\begin{array}{l}
A=b c \\
B=c a \\
C=a b
\end{array}\right.
$$

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