
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
Calculate the following:

\\(⑴\\) Calculate \\({{27}^{\\frac{2}{3}}}-{{2}^{{{\\log }_{4}}3}}\\times {{\\log }_{2}}\\dfrac{1}{8}+{{\\log }_{2}}3\\times {{\\log }_{3}}4\\);

\\((2)\\) Given \\(\\cos \\alpha =\\dfrac{5}{13}\\), and angle \\(\\alpha \\) is in the fourth quadrant, find the values of \\(\\sin \\alpha \\) and \\(\\tan \\alpha \\).

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