
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 sine of angle $\mathrm{A}$ is $\frac{\sqrt{3}}{2}$. Point M is taken on side $\mathrm{AC}$ such that $\mathrm{CM}=b$, and point N is taken on side $\mathrm{AB}$ such that $\mathrm{BN}=a$. Let $\mathrm{T}$ be the midpoint of $\mathrm{NC}$, and $\mathrm{P}$ be the midpoint of $\mathrm{BM}$. Find the length of $\mathrm{PT}$.

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