
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
Suppose \( P \) is an integer and \( 5 < P < 20 \). If the roots of the equation \( x^{2} - 2(2P - 3)x + 4P^{2} - 14P + 8 = 0 \) are integers, find the value of \( P \).

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