
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 solution process of the following question:<br/>$\begin{array}{l}x^{2}+8x+7\\=(x^{2}+8x+16)-16+7(\text{add 16 first, then subtract 16})\\=(x+4)^{2}-3^{2}\;\;\;\;(\text{using the formula for perfect square})\\=(x+4+3)(x+4-3)\;(\text{using the formula for difference of squares})\\=(x+7)(x+1)\end{array}$<br/>Also, like:<br/>$\begin{array}{l}x^{2}-4x-5\\=(x^{2}-4x+4)-4-5\\=(x-2)^{2}-3^{2}\;\;\;\;\\=(x-2+3)(x-2-3)\;\\=(x+1)(x-5)\end{array}$<br/>Using the method of adding and subtracting terms to factorize polynomials into perfect squares, please use the above method to factorize the following polynomials:<br/>①$x^{2}+6x+5$；<br/>②$m^{2}-m-12$.

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