
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
Reading material: The cosine theorem is a mathematical theorem that describes the relationship between the lengths of the three sides of a triangle and the cosine value of an angle. It can be used to solve problems where two sides and an included angle of a triangle are known to find the third side, or when all three sides are known to find an angle. The cosine theorem is described as follows: In triangle $\triangle ABC$, with angles $\angle A$, $\angle B$, and $\angle C$ opposite sides $a$, $b$, and $c$ respectively, the square of any side of the triangle is equal to the sum of the squares of the other two sides minus twice the product of those two sides and the cosine of the included angle. This can be expressed in formulas as: $a^{2}=b^{2}+c^{2}-2bc\cos A$, $b^{2}=a^{2}+c^{2}-2ac\cos B$, $c^{2}=a^{2}+b^{2}-2ab\cos C$. Now, given in triangle $\triangle ABC$, $AB=3$, $AC=4$, and $\angle A=60^{\circ}$, find $BC$.

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