
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 $ABC$, point $M$ is taken such that $BM:MC=2:5$. The bisector $BL$ of the triangle intersects segment $AM$ 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) A point $F$ is marked on segment $MC$ such that $MF:FC=1:4$. It is additionally known that lines $LF$ and $BC$ are perpendicular. Find the angle $CBL$.

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