
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
For which values of the parameter \( a \) does the equation \( f(x) = p(x) \) have one solution, if \( f(x) = \left|\frac{2 x^{3}-5 x^{2}-2 x+5}{(1.5 x-3)^{2}-(0.5 x-2)^{2}}\right| \) and \( p(x) = |2 x+5|+a \)? If there is more than one value for the parameter, indicate the sum of these values.

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