
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
Factorize the following expressions:<br/>$(1)8x^{2}+26xy-15y^{2}$;<br/>$(2)x^{6}-y^{6}-2x^{3}+1$;<br/>$(3)a^{3}+a^{2}c+b^{2}c-abc+b^{3}$;<br/>$(4)x^{3}-11x^{2}+31x-21$.

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