Orach LeChayim of Zlotchov zt'l teaches, "A person must believe in his tefillah, and know that it accomplishes in heaven... He must know that... he has the power to overturn the midas hadin to midas harachamim. This is the meaning of the pasuk (Devarim 32:20) המה תהפוכות דור; It’s a generation that can turn midas hadin to rachamim. The problem is, בם אמון לא בנים, they don't believe they have this ability."
On Yom Kippur, the kohen gadol came into the Kodesh Kadoshim with ומחתה כף, a large spoon and a shovel. The shovel contained coals from the mizbeach, and the spoon held the ketores. He put the coals on the ground, in the Kodesh Kadoshim, and poured the ketores over the coals. He then left the spoon and shovel in the Kodesh Kadoshim and went out to perform the rest of the avodah. At the end of the avodah, he returned to remove the spoon and shovel. Now, we understand why he initially left the מחתה, the shovel, in the Kodesh Kadoshim. He did so because the ketores was being offered on the coals. It was too early to take out the shovel. But why didn't he immediately remove the כף, the empty spoon? Why did he only take it out at the end of the avodah?
Reb Yechezkel Abramsky zt'l answers that after offering the ketores in the Kodesh Kadoshim, the kohen gadol said a short tefillah for Klal Yisrael, outside the Kodesh Kadoshim. It isn't proper to hold anything while davening. He, therefore, left the spoon behind. We can add that one certainly shouldn't hold anything on his mind or heart when he is davening. His full kavanah should be on the tefillah.
Tefillah during the Aseres Yemei Teshuvah is incredibly potent. The Rambam (Teshuvah 2:6) writes, "Although teshuvah and shouting [out to Hashem] are always good, during the ten days between Rosh Hashanah and Yom Kippur, teshuvah and tefillah are far better and are accepted immediately...."