
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
In triangle $\triangle ABC$, $a+b=11$. Choose one of the following two conditions as known, and find:<br/>$(Ⅰ)$ the value of $a$;<br/>$(Ⅱ)$ $\sin C$ and the area of $\triangle ABC$.<br/>Condition 1: $c=7$, $\cos A=-\frac{1}{7}$;<br/>Condition 2: $\cos A=\frac{1}{8}$, $\cos B=\frac{9}{16}$.<br/>Note: If both conditions 1 and 2 are answered separately, the first answer will be scored.

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