
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 following system of equations:

$$
\begin{gathered}
x + y = a \\
z + t = b \\
xy = zt \\
x^3 + y^3 + z^3 + t^3 = c
\end{gathered}
$$

Application: \(a = 10\), \(b = 5\), \(c = 1080\).

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