
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 practice class, when solving the equation $\frac{{2x-1}}{5}+1=\frac{{x+a}}{2}$, Xiao Li made a mistake by not multiplying the $1$ on the left side of the equation by $10$ when clearing the denominators. As a result, the solution obtained for the equation is $x=4$. Find the value of $a$ and determine the correct solution to the original equation.

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