
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 that $\tan \theta = -\frac{3}{4}$, find the value of $1 + \sin \theta \cos \theta - \cos^2 \theta$.
(2) Evaluate the expression $\frac{\cos 40^{\circ} + \sin 50^{\circ}(1 + \sqrt{3}\tan 10^{\circ})}{\sin 70^{\circ} \sqrt{1 + \sin 50^{\circ}}}$.

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