To the United States: do not add fuel to the flames
Even with the United Nations Security Council’s resolution on the Korean Peninsula issue, and has legitimate concerns over the nuclear non-proliferation and security issues, unilateral sanctions from the United States against the DPRK which are beyond the UN resolutions would be counterproductive and will add pressure to the situation.
For decades, sanctions, pressure, isolation against the DPRK initiated by the United States is one of the root causes of conflicts on the peninsula. Since the 1990s, U.S. government policy toward the DPRK has swung between engagement and isolation, making the DPRK doubtful of the sincerity of the United States, and giving an excuse to the DPRK in violation of the agreement.
The United States, as the superpower whose comprehensive national and military strength is far stronger than the DPRK's, is in a strong position; therefore, any strong move will only increase tension on the peninsula.
To South Korea: do not miss the focus
With the "protective umbrella" provided by the U.S., South Korea’s security is still fragile. Due to the geographical location and military deployment, South Korea would become the biggest victim if any conflicts and wars break out on the peninsula.
The south and north peninsula have had a period of increased contacts and exchanges, and South Korea's new government has repeatedly expressed its willingness to implement policy toward the DPRK which are different from the Lee Myung-bak government.
Being one of the major parties of the Korean Peninsula issue, South Korea should play the role to cool down the tensions on the Korean Peninsula, rather than pushed by the DPRK or the United States.