
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
An isosceles triangle $\triangle ABC$ with $AB = AC$ and side lengths $AB = AC = s$ and $BC = t$, has a unique point $P$ inside it such that $AP=2$, $BP=\sqrt{5}$, and $CP=3$. Find the values of $s$ and $t$.
A) $s = \sqrt{7}, t = \sqrt{5}$
B) $s = 2\sqrt{3}, t = \sqrt{3}$
C) $s = 2\sqrt{3}, t = \sqrt{5}$
D) $s = 3, t = \sqrt{5}$
E) $s = 3\sqrt{3}, t = 2\sqrt{5}$

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