
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
Find all quadruples \((a, b, c, d)\) of positive integers which satisfy

\[ 
\begin{aligned}
a b+2 a-b &= 58, \\
b c+4 b+2 c &= 300, \\
c d-6 c+4 d &= 101.
\end{aligned}
\]

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