Advance

v.hopeful, capableprofessional

Meaning 1

To move nearer to a position, place, or desired result.

Reach for it when describing concrete forward progress toward an objective

Daily testing will advance the project from prototype to public trial.

everyday
progress
gradual improvement matters without naming an agent
not when Progress can happen naturally while advance often signals directed movement.
warm
move forward
plain encouraging language suits a shared effort
not when This phrase lacks precision about what actually improved.
professional
accelerate
increasing the rate of progress is the achievement
not when Acceleration is wrong when movement is steady but not faster.
professional
develop
skills, plans, or systems become more mature
not when Development can expand sideways without nearing a goal.
literary
forge ahead
determined progress continues despite resistance
not when The martial energy may overpower a cooperative context.

To actively put forward or support an idea, claim, or cause.

Reach for it when naming deliberate advocacy that brings an argument into consideration

The report advances a practical case for restoring the footpath.

warm
champion
visible personal commitment drives support for a cause
not when Champion is too personal when a document merely presents a claim.
professional
promote
you actively increase support or visibility
not when Promote can sound commercial when the subject is an argument.
formal
propose
an idea is formally offered for consideration
not when A proposal may be stated once without sustained advocacy.

advance steadily
Repairs advance steadily whenever the tide is low.
advance a cause
The concert will advance a cause the musicians value.
advance knowledge
Open field notes advance knowledge beyond a single laboratory.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.