
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. Compute the following expression: \\
   $(\dfrac{4}{9})^{-\dfrac{3}{2}}+(\left(-2\right)^6)^{\dfrac{1}{2}}-\lg 0.4-2\lg 0.5-14\times\log_2 \sqrt{2}$ \\
2. Given a point $P(\sin \alpha,\cos \alpha)$ situated on the line $y=\dfrac{1}{2}x$, find the value of $\dfrac{\cos (\pi-\alpha)+\sin (\pi+\alpha)}{\cos (\dfrac{1}{2}\pi-\alpha)+\sin (\dfrac{1}{2}\pi+\alpha)}+2\sin \alpha\cos \alpha$.

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