
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
Let $L$ be the line with slope $\frac{5}{12}$ that contains the point $A=(24,-1)$, and let $M$ be the line perpendicular to line $L$ that contains the point $B=(5,6)$.  The original coordinate axes are erased, and line $L$ is made the $x$-axis and line $M$ the $y$-axis.  In the new coordinate system, point $A$ is on the positive $x$-axis, and point $B$ is on the positive $y$-axis.  The point $P$ with coordinates $(-14,27)$ in the original system has coordinates $(\alpha,\beta)$ in the new coordinate system.  Find $\alpha+\beta$.

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