
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  $ABC$  be a triangle in which ( ${BL}$ is the angle bisector of  ${\angle{ABC}}$   $\left( L\in AC \right)$ ,  ${AH}$  is an altitude of $\vartriangle ABC$   $\left( H\in BC \right)$  and  ${M}$ is the midpoint of the side  ${AB}$ . It is known  that the midpoints of the segments  ${BL}$  and  ${MH}$  coincides. Determine the internal angles of triangle  $\vartriangle ABC$ .

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