
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 the morning, Esther biked from home to school at an average speed of  $x$  miles per hour.  In the afternoon, having lent her bike to a friend, Esther walked back home along the same route at an average speed of 3 miles per hour.  Her average speed for the round trip was 5 miles per hour.  What is the value of  $x$ ?

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