
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 $\triangle ABC$, the lengths of the sides opposite to the internal angles A, B, and C are $a$, $b$, and $c$ respectively, and it is given that $b=3$, $c=1$. The area of $\triangle ABC$ is $\sqrt{2}$. Find the values of $\cos A$ and $a$.
(The area of $\triangle ABC$, $S_{\triangle ABC} = \frac{1}{2}bc\sin A = \frac{1}{2}ab\sin C = \frac{1}{2}ac\sin B$)

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