
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
In triangle $\mathrm{ABC}$, the angle bisectors of angles $\mathrm{BAC}$ and $\mathrm{BCA}$ intersect sides $\mathrm{BC}$ and $\mathrm{AB}$ at points $K$ and $P$ respectively. It is known that the length of side $AC$ is equal to the sum of the lengths of segments $AP$ and $CK$. Find the measure of angle $\mathrm{ABC}$.

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