
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:
\[
\begin{cases} 
ab + a + 2b = 78 \\ 
bc + 3b + c = 101 \\ 
cd + 5c + 3d = 232 \\ 
de + 4d + 5e = 360 \\ 
ea + 2e + 4a = 192 
\end{cases}
\]

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