
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
In a math class, Bingbing made a mistake while solving the equation involving $x$: $\frac{2x-1}{5}+1=\frac{x+a}{2}$. Due to carelessness, she forgot to multiply the $1$ on the left side by $10$ when clearing the denominators, resulting in the solution $x=-6$. Find the value of $a$ and the solution to the original equation.

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