
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 all values of the parameter \( a \) for which the inequality 
\[ \log _{\sqrt{a / 10}}\left(\frac{a+8x-x^{2}}{20}\right) \geq 2 \]
has at least one solution \( x \geq 2 \), and every solution of the inequality is also a solution of the equation 
\[ |a+2x-16| + |a-2x+9| = |2a-7|. \]

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