Great responses below (minus mike the so called "real estate pro"). .
For that reason, from the perspective of paying taxes, the lower your assessed value, the better. It means you'll pay less in taxes.
You say several times that you believe the assessed value is lower than what you think the fair market value is for your house. That's good for you. If your assessment goes up, so will your taxes.
The purpose of assessed value is so the county treasurer can collect taxes. Assessing real property is big job, so most counties re-assess on full transfer, and "as needed".
Most counties also have an appeal system so if you can prove that your property is worth less, then you can have your assessment changed. Curiously, I did check on line and did not find an assessor's website. Most Counties have a pretty simply system for appealing assessed values.
Plus, town assessments are typically 2-3 years behind current market values. The market is fluid and constantly changing. Town Assessors couldn't possibly keep up with the current market trends,
If you want a true current market value of your home, call in a few local real estate agents to perform a CMA (competitive market analysis) for free. Or better yet, hire an appraiser (around $300 for a single family) to tell you what the appraised value would be (don't confuse assessed value and appraised value).
Barbara from Memphis is right. Typically assessed values should be lower than true market values, but with the declining markets we've seen here in MA, it's best to check for sure!