Sell Own Currency = Strengthen Currency ? (Econ)

Been pulling my hair over this question for Econs in the Qbank -

Developing country maintains fixed currency value relative to USD is experiencing decline in economic activity, and inflation falls below that of the US.

The most likely result of the developing country’s (ie. ABC) actions to maintain the fixed rate is: (Ans) that short term interest rates will fall…

the others were: foreign reserves will decrease (i chose this), money supply will contract

My reasoning for not choosing the correct option is as follows:
-economy & inflation drop = prices drop
-ABC weakens against USD
-ABC/USD rise
-must lower to keep target (ie. strengthen ABC’s currency)
-need to increase demand for ABC
-buy more ABC currency, sell foreign reserves

what was the mistake in my reasoning? i went onto various sites which said that to strengthen own currency, the central bank should buy it and sell foreign reserves… thanks!

What does the solution say?

If I go by the question, a decline in economic activity would lead to a deficient demand for ABC currency, leading to foreign investors pulling out their capital from that country (i.e. sell ABC, take USD and get out), leading to a decline in foreign currency reserves. And if the monetary authority continues to buy ABC and sell foreign reserves, that will lead to a devaluation if market participants believe that the reserves are insufficient to sustain the parity.

So the result is for short-term interest rates to fall (money supply expanding), so that it will increase private demand for domestic currency (leading to higher consumption and spending), leading to higher economic activity. This will lead to accelerating inflation but since the case stated that inflation was below of US, the increase in inflation (as a result of higher spending) would not cause too much problem.

Thank you @fino_abama !

Your explanation makes it clear now.

The solution is not dissimilar to yours but explains it in a way that is not easy to understand:
-decline in econ & domestic inflation, ABC rises against USD
-to protect target, central bank will purchase foreign reserves & sell ABC (not sure why)
-thus Domestic money supply increase
-thus ST interest rates decrease
-thus foreign reserves increase