
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
Two motorboats with the same own speed depart from points $A$ and $B$ heading towards each other. If the first boat, traveling against the current, increases its own speed by $x$ kilometers per hour, and the second boat, traveling with the current, decreases its speed by the same amount, then the first boat will arrive at point $A$ earlier by the same number of hours that the second boat will be late to arrive at point $B$. Determine $x$, if the speed of the river current is $a$ kilometers per hour.

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