
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
The function  $f(x) = x^2 + (2a + 3)x + (a^2 + 1)$  only has real zeroes. Suppose the smallest possible value of  $a$  can be written in the form  $p/q$ , where  $p, q$  are relatively prime integers. Find  $|p| + |q|$ .

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