
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
On the side $BC$ of triangle $ABC$, a point $M$ is chosen such that $BM:MC = 3:7$. The angle bisector $BL$ of this triangle and the segment $AM$ intersect at point $P$ at a $90^{\circ}$ angle.

a) Find the ratio of the area of triangle $ABP$ to the area of quadrilateral $LPMC$.

b) On segment $MC$, a point $T$ is marked such that $MT:TC = 1:6$. Additionally, it is known that lines $LT$ and $BC$ are perpendicular. Find the angle $CBL$.

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