
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
(1) Complete the following square problem: $x^2 + 2px + 1 = [x^2 + 2px + (\quad)] + (\quad) = (x + \quad)^2 + (\quad)$  
(2) Factorize: $a^2 - b^2 + 4a + 2b + 3$ The result is $\quad$.

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