
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
There are two forces \( f_{1} \) and \( f_{2} \) acting on the origin \( O \) of a coordinate axis,
$$
\begin{array}{l}
\vec{f}_{1}=\overrightarrow{O A}=\sqrt{2}\left(\cos 45^{\circ}+i \sin 45^{\circ}\right), \\
\overrightarrow{f_{2}}=\overrightarrow{O B}=2\left[\cos \left(-30^{\circ}\right)+i \sin \left(-30^{\circ}\right)\right].
\end{array}
$$
(1) Find the magnitude and direction of their resultant force.  
(2) Find the distance between points \( A \) and \( B \) (accurate to 0.1).

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