
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
(1) Given $\sin\left( \alpha +\frac{\pi }{4} \right)=\frac{\sqrt{2}}{10}$, with $\alpha\in(0,\pi)$, find the value of $\cos \alpha$;

(2) Evaluate: $\left( \tan {10^{\circ} }-\sqrt{3} \right)\sin {40^{\circ} }$.

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