
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
1. If \(\left|\begin{array}{ll}a & b \\ c & d\end{array}\right|=a d-b c\) and \(\left|\begin{array}{ll}3 & 4 \\ 2 & k\end{array}\right|=k\), find \(k\).
2. If \(50 m=54^{2}-k^2\), find \(m\).
3. If \((m+6)^{a}=2^{12}\), find \(a\).
4. \(A, B\) and \(C\) are the points \((a, 5),(2,3)\) and \((4, b)\) respectively. If \(A B \perp B C\), find \(b\).

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