
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

Find the solution for the system of equations:

1) \( 5(x+4) - 7(a+2) = 0 \)
2) \( x^2 + 2x - 24 + \left( \frac{|x+1|}{x+1} + \frac{|x-3|}{x-3} + a \right)^2 = 0 \) 

or equivalently 

\[ (x+1)^2 + \left( \frac{|x+1|}{x+1} + \frac{|x-3|}{x-3} + a \right)^2 = 25 \]

Note the domain of validity (ОДЗ in Russian):
- \( x \neq -1 \)
- \( x \neq 3 \)
- \( 5x - 7a + 6 \geq 0 \)

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