The gemora in Brochos (32b) explains “chazak” – strengthen yourself through Torah study and “v’ematz” – strengthen yourself through performing good deeds.
The sefer Mishbtzos Zahav offers that “chazak” refers to mustering the energy and focus to constantly seek out more in our avodas (service of) Hashem, while “v’ematz” refers to to the fortitude needed not to give up hope for what we have not yet attained despite great effort to advance in our service of Hashem.
This need to have perseverance in serving Hashem is the focus of the Chofetz Chaim (Devarim 4,41).
Many times we need to invoke the possuk in Mishlei (2, 4), “Im t’vakshena k’kesef” – “If you seek it (the Torah) out like silver.” The Chofetz Chaim offers a moshol: If a person was walking on the sea shore and saw small pieces of silver wash up, wouldn’t he gather as much as he could despite the fact that he could not gather every piece? Surely, even a little silver is better than none! So too, as servants of Hashem we must focus on all the small gains in our knowledge and spiritual growth. We must realize that each bit is precious and valuable.
Similarly, “v’chamatmonim tachp’senah” – “And like that which is hidden - search for it.” Even if our efforts to mine gems hour after hour might seem to be in vain, we plug away with the hope that it will be worth it in the end. In the same way, “v’ematz’” means plug away hour after hour in avodas Hashem even if we don’t see advancement. We can be sure, as Hashem guarantees Yehuoshua, it will be worth it.
As we begin a new cycle of Nach Yomi “chazak v”ematz” - May Hashem help us sustain the yearning to learn, to know and to live Nach, while strengthening our resolve to learn our chapter a day, hard or easy, searching for gems and having patience in finding them.