
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
The road between settlements $A$ and $B$ first has an uphill and then a downhill section. A cyclist, traveling on the downhill section at a speed $a$ km/h faster than on the uphill section, takes exactly $t$ hours to travel from $A$ to $B$, and half that time to return from $B$ to $A$. Find the cyclist's speed on the uphill and downhill sections if the distance between the settlements is $b$ km.

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