
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
Read the following text and examples: Grouping and factoring out common factors or using formulas to continue factoring is called grouping factoring. For example, the factoring method of the following two expressions is called grouping factoring:<br/>$(1)am+an+bm+bn=\left(am+bm\right)+\left(an+bn\right)=m\left(a+b\right)+n\left(a+b\right)=\left(a+b\right)\left(m+n\right)$;<br/>$(2)x^{2}-y^{2}-2y-1=x^{2}-(y^{2}+2y+1)=x^{2}-\left(y+1\right)^{2}=\left(x+y+1\right)\left(x+y-1)$<br/>Try factoring using the above method:<br/>$(1)a^{2}+2ab+b^{2}+ac+bc$;<br/>$(2)4a^{2}-x^{2}+4xy-4y^{2}$.

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